Edit Profile (opens in new tab) Macbeath, A. Murray Co-Author Distance Author ID: macbeath.a-murray Published as: Macbeath, A. M.; Macbeath, A. Murray External Links: MGP · Wikidata Documents Indexed: 48 Publications since 1947, including 1 Book 1 Further Contribution Co-Authors: 7 Co-Authors with 11 Joint Publications 89 Co-Co-Authors all top 5 Co-Authors 37 single-authored 3 Rogers, Claude Ambrose 3 Świerczkowski, Stanisław S. 1 Başkan, Turgut 1 Beardon, Alan Frank 1 Earle, Clifford J. 1 Harvey, William James 1 Henstock, Ralph 1 Hoare, A. Howard M. 1 Jack, Henry 1 Lehner, Joseph 1 Lehto, Olli E. 1 Marden, Albert 1 Maskit, Bernard 1 Rankin, Robert Alexander 1 Singerman, David 1 Swinnerton-Dyer, Peter all top 5 Serials 10 Proceedings of the Cambridge Philosophical Society 4 Canadian Journal of Mathematics 3 Proceedings of the Edinburgh Mathematical Society. Series II 3 Proceedings of the London Mathematical Society. Third Series 3 Journal of the London Mathematical Society 3 Proceedings of the Glasgow Mathematical Association 2 Mathematical Proceedings of the Cambridge Philosophical Society 2 Bulletin of the London Mathematical Society 2 Duke Mathematical Journal 2 The Quarterly Journal of Mathematics. Oxford Second Series 2 Annals of Mathematics. Second Series 1 Fundamenta Mathematicae 1 Glasgow Mathematical Journal 1 Illinois Journal of Mathematics 1 Journal of the London Mathematical Society. Second Series 1 Nederlandse Akademie van Wetenschappen. Proceedings. Series A. Indagationes Mathematicae 1 The Edinburgh Mathematical Notes all top 5 Fields 12 Number theory (11-XX) 9 Group theory and generalizations (20-XX) 7 Functions of a complex variable (30-XX) 4 Topological groups, Lie groups (22-XX) 2 Combinatorics (05-XX) 2 Measure and integration (28-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Differential geometry (53-XX) 2 Manifolds and cell complexes (57-XX) 1 History and biography (01-XX) 1 Field theory and polynomials (12-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Geometry (51-XX) 1 General topology (54-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 36 Publications have been cited 614 times in 539 Documents Cited by ▼ Year ▼ The classification of non-euclidean plane crystallographic groups. Zbl 0183.03402 Macbeath, A. M. 131 1967 Generators of the linear fractional groups. Zbl 0192.35703 Macbeath, A. M. 66 1969 On a theorem of Hurwitz. Zbl 0134.16603 Macbeath, A. M. 60 1961 Action of automorphisms of a compact Riemann surface on the first homology group. Zbl 0259.30016 Macbeath, A. M. 40 1973 On the measure of sum-sets. I. The theorems of Brunn, Minkowski and Lusternik. Zbl 0052.18302 Henstock, Ralph; Macbeath, A. M. 40 1953 On a curve of genus 7. Zbl 0146.42705 Macbeath, A. M. 39 1965 Groups of homeomorphisms of a simply connected space. Zbl 0122.17503 Macbeath, A. M. 35 1964 Spaces of subgroups and Teichmüller space. Zbl 0314.32012 Macbeath, A. M.; Singerman, D. 35 1975 A compactness theorem for affine equivalence-classes of convex regions. Zbl 0042.16401 Macbeath, A. M. 30 1951 An extremal property of the hypersphere. Zbl 0042.40801 Macbeath, A. M. 18 1951 On measure of sum sets. II. The sum-theorem for the torus. Zbl 0052.26301 Macbeath, A. M. 16 1953 A theorem on non-homogeneous lattices. Zbl 0047.04903 Macbeath, A. M. 11 1952 Discrete groups and automorphic functions. Proceedings of an instructional conference organized by the London Mathematical Society and the University of Cambridge (a NATO Advanced Study Institute). Zbl 0411.30033 10 1977 On the set of generators of a subgroup. Zbl 0118.26503 Macbeath, A. M.; Swierczkowski, S. 9 1959 Packings, free products and residually finite groups. Zbl 0118.03204 Macbeath, A. M. 9 1963 Factorization of matrices and Minkowski’s conjecture. Zbl 0098.26303 Macbeath, A. M. 8 1961 Commensurability of co-compact three-dimensional hyperbolic groups. Zbl 0588.22009 Macbeath, A. M. 8 1983 Residual nilpotency of Fuchsian groups. Zbl 0539.20026 Macbeath, A. M. 6 1984 Groups of hyperbolic crystallography. Zbl 0338.20056 Macbeath, A. M.; Hoare, A. H. M. 6 1976 Siegel’s mean value theorem in the geometry of numbers. Zbl 0080.26601 Macbeath, A. M.; Rogers, C. A. 6 1958 On a theorem by J. Nielsen. Zbl 0128.30301 Macbeath, A. M. 6 1962 Limits of lattices in a compactly generated group. Zbl 0097.03301 Macbeath, A. M.; Swierczkowski, S. 5 1960 Hurwitz groups and surfaces. Zbl 0965.30013 Macbeath, A. Murray 4 1999 Extensions of the rationals with Galois group \(\mathrm{PGL}(2,\mathbb Z_n)\). Zbl 0184.07603 Macbeath, A. M. 4 1969 A new sequence of minima of minima in the geometry of numbers. Zbl 0042.04602 Macbeath, A. M. 4 1951 Centralizers of reflections in crystallographic groups. Zbl 0487.20034 Baskan, T.; Macbeath, A. M. 3 1982 The volume of a certain set of matrices. Zbl 0087.01903 Jack, Henry; Macbeath, A. M. 3 1959 On convex fundamental regions for a lattice. Zbl 0103.27603 Macbeath, A. M. 2 1961 On the measure of product sets in a topological group. Zbl 0116.26302 Macbeath, A. M. 2 1960 Generic Dirichlet polygons and the modular group. Zbl 0582.30031 Macbeath, A. M. 2 1985 Superimprimitive 2-generator finite groups. Zbl 0627.20003 Macbeath, A. M. 1 1987 A modified form of Siegel’s mean-value theorem. Zbl 0065.28101 Macbeath, A. M.; Rogers, C. A. 1 1955 Measures in homogeneous spaces. Zbl 0096.02201 Macbeath, A. M.; Świerczkowski, S. 1 1960 On measure of sumsets. III: The continuous \((\alpha+\beta)\)-theorem. Zbl 0112.28501 Macbeath, A. M. 1 1961 Non-convex regions in three and more dimensions. Zbl 0032.40301 Macbeath, A. M. 1 1949 Non-homogeneous lattices in the plane. Zbl 0049.16501 Macbeath, A. M. 1 1952 Hurwitz groups and surfaces. Zbl 0965.30013 Macbeath, A. Murray 4 1999 Superimprimitive 2-generator finite groups. Zbl 0627.20003 Macbeath, A. M. 1 1987 Generic Dirichlet polygons and the modular group. Zbl 0582.30031 Macbeath, A. M. 2 1985 Residual nilpotency of Fuchsian groups. Zbl 0539.20026 Macbeath, A. M. 6 1984 Commensurability of co-compact three-dimensional hyperbolic groups. Zbl 0588.22009 Macbeath, A. M. 8 1983 Centralizers of reflections in crystallographic groups. Zbl 0487.20034 Baskan, T.; Macbeath, A. M. 3 1982 Discrete groups and automorphic functions. Proceedings of an instructional conference organized by the London Mathematical Society and the University of Cambridge (a NATO Advanced Study Institute). Zbl 0411.30033 10 1977 Groups of hyperbolic crystallography. Zbl 0338.20056 Macbeath, A. M.; Hoare, A. H. M. 6 1976 Spaces of subgroups and Teichmüller space. Zbl 0314.32012 Macbeath, A. M.; Singerman, D. 35 1975 Action of automorphisms of a compact Riemann surface on the first homology group. Zbl 0259.30016 Macbeath, A. M. 40 1973 Generators of the linear fractional groups. Zbl 0192.35703 Macbeath, A. M. 66 1969 Extensions of the rationals with Galois group \(\mathrm{PGL}(2,\mathbb Z_n)\). Zbl 0184.07603 Macbeath, A. M. 4 1969 The classification of non-euclidean plane crystallographic groups. Zbl 0183.03402 Macbeath, A. M. 131 1967 On a curve of genus 7. Zbl 0146.42705 Macbeath, A. M. 39 1965 Groups of homeomorphisms of a simply connected space. Zbl 0122.17503 Macbeath, A. M. 35 1964 Packings, free products and residually finite groups. Zbl 0118.03204 Macbeath, A. M. 9 1963 On a theorem by J. Nielsen. Zbl 0128.30301 Macbeath, A. M. 6 1962 On a theorem of Hurwitz. Zbl 0134.16603 Macbeath, A. M. 60 1961 Factorization of matrices and Minkowski’s conjecture. Zbl 0098.26303 Macbeath, A. M. 8 1961 On convex fundamental regions for a lattice. Zbl 0103.27603 Macbeath, A. M. 2 1961 On measure of sumsets. III: The continuous \((\alpha+\beta)\)-theorem. Zbl 0112.28501 Macbeath, A. M. 1 1961 Limits of lattices in a compactly generated group. Zbl 0097.03301 Macbeath, A. M.; Swierczkowski, S. 5 1960 On the measure of product sets in a topological group. Zbl 0116.26302 Macbeath, A. M. 2 1960 Measures in homogeneous spaces. Zbl 0096.02201 Macbeath, A. M.; Świerczkowski, S. 1 1960 On the set of generators of a subgroup. Zbl 0118.26503 Macbeath, A. M.; Swierczkowski, S. 9 1959 The volume of a certain set of matrices. Zbl 0087.01903 Jack, Henry; Macbeath, A. M. 3 1959 Siegel’s mean value theorem in the geometry of numbers. Zbl 0080.26601 Macbeath, A. M.; Rogers, C. A. 6 1958 A modified form of Siegel’s mean-value theorem. Zbl 0065.28101 Macbeath, A. M.; Rogers, C. A. 1 1955 On the measure of sum-sets. I. The theorems of Brunn, Minkowski and Lusternik. Zbl 0052.18302 Henstock, Ralph; Macbeath, A. M. 40 1953 On measure of sum sets. II. The sum-theorem for the torus. Zbl 0052.26301 Macbeath, A. M. 16 1953 A theorem on non-homogeneous lattices. Zbl 0047.04903 Macbeath, A. M. 11 1952 Non-homogeneous lattices in the plane. Zbl 0049.16501 Macbeath, A. M. 1 1952 A compactness theorem for affine equivalence-classes of convex regions. Zbl 0042.16401 Macbeath, A. M. 30 1951 An extremal property of the hypersphere. Zbl 0042.40801 Macbeath, A. M. 18 1951 A new sequence of minima of minima in the geometry of numbers. Zbl 0042.04602 Macbeath, A. M. 4 1951 Non-convex regions in three and more dimensions. Zbl 0032.40301 Macbeath, A. M. 1 1949 all cited Publications top 5 cited Publications all top 5 Cited by 528 Authors 31 Bujalance, Emilio 24 Gromadzki, Grzegorz 19 Costa Gonzáles, Antonio Félix 17 Conder, Marston Donald Edward 15 Martinez, Ernesto C. 14 Etayo Gordejuela, José Javier 12 Cirre, Francisco-Javier 12 May, Coy L. 11 Izquierdo, Milagros 10 Tyszkowska, Ewa 8 Jones, Gareth A. 8 Reyes-Carocca, Sebastián 8 Singerman, David 7 Estrada, Beatriz 7 Nedela, Roman 7 Zimmermann, Bruno P. 6 Hidalgo, Rubén Antonio 6 Wootton, Aaron 5 Broughton, S. Allen 5 Gamboa Mutuberria, José Manuel 5 Gruber, Peter Manfred 5 Kozłowska-Walania, Ewa 5 Macbeath, A. Murray 5 Melekoğlu, Adnan 5 Szirmai, Jenó 4 Bacelo, Adrián 4 Bárány, Imre 4 Bujalance, José A. 4 Forrester, Peter J. 4 Groemer, Helmut 4 Klee, Victor LaRue 4 Mednykh, Aleksandr Dmitrievich 4 Mednykh, Il’ya Aleksandrovich 4 Molnár, Emil 4 Reid, Alan W. 4 Širáň, Jozef 4 Škoviera, Martin 4 Tamburini, Maria Chiara 4 Turbek, Peter 4 Vsemirnov, Maxim 4 Zimmerman, Jay J. 3 Bagiński, Czesław 3 Gritzmann, Peter 3 Hamrouni, Hatem 3 Klartag, Bo’az 3 Kwak, Jin Ho 3 Larman, David G. 3 Lučić, Zoran 3 McCullough, Darryl 3 Monod, Nicolas 3 Morifuji, Takayuki 3 Mushtaq, Qaiser 3 Neumann, Walter David 3 Pellegrini, Marco Antonio 3 Porto, Ana Maria 3 Salani, Paolo 3 Satomi, Takashi 3 Schütt, Carsten 3 Surowski, David B. 3 Szepietowski, Błażej 3 Zieschang, Heiner 2 Aggarwal, Satish Kumar 2 Antonyan, Sergey A. 2 Barthe, Franck 2 Barthel, Woldemar 2 Bennett, Curtis D. 2 Bobkov, Sergey Germanovich 2 Bokowski, Jürgen G. 2 Böröczky, Karoly jun. 2 Brin, Matthew G. 2 Caprace, Pierre-Emmanuel 2 Carocca, Angel 2 Chazelle, Bernard 2 Chen, Su-Shing 2 Chen, William Yun 2 Cortázar, Ismael 2 de Roton, Anne 2 del Río, Angel 2 Dinghas, Alexander 2 Du, Shaofei 2 Dumir, Vishwa Chander 2 Fainleib, A. S. 2 Galicer, Daniel 2 Georgakopoulos, Agelos 2 Gévay, Gábor E. 2 Gilman, Jane P. 2 Girondo, Ernesto 2 González-Diez, Gabino 2 Gözütok, Nazlı Yazıcı 2 Griesmer, John T. 2 Güler, Bahadır Özgür 2 Gupta, Dharma P. 2 Hoare, A. Howard M. 2 Hughes, Sam 2 Jespers, Eric 2 Kato, Takao 2 Kellendonk, Johannes 2 Khrabrov, A. I. 2 Kiefer, Ann 2 Kolbe, Benedikt ...and 428 more Authors all top 5 Cited in 161 Serials 34 Journal of Algebra 21 Journal of Pure and Applied Algebra 20 Mathematische Annalen 17 Archiv der Mathematik 17 Mathematische Zeitschrift 15 Proceedings of the American Mathematical Society 13 Israel Journal of Mathematics 13 Glasgow Mathematical Journal 13 Transactions of the American Mathematical Society 10 Advances in Mathematics 10 Geometriae Dedicata 10 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 9 Journal of Number Theory 9 Topology and its Applications 9 Discrete & Computational Geometry 8 Revista Matemática Iberoamericana 7 Communications in Algebra 7 Journal of Soviet Mathematics 7 Manuscripta Mathematica 7 Mathematika 7 European Journal of Combinatorics 7 Acta Mathematica Sinica. English Series 6 Mathematical Proceedings of the Cambridge Philosophical Society 5 Acta Mathematica 5 Monatshefte für Mathematik 5 Revista Matemática Complutense 5 Journal of Algebra and its Applications 4 Discrete Mathematics 4 Mathematical Notes 4 Rocky Mountain Journal of Mathematics 4 Annali di Matematica Pura ed Applicata. Serie Quarta 4 Duke Mathematical Journal 4 Journal of Combinatorial Theory. Series B 4 Proceedings of the Edinburgh Mathematical Society. Series II 4 International Journal of Mathematics 4 Bulletin of the American Mathematical Society. New Series 4 Experimental Mathematics 4 Annals of Mathematics. Second Series 4 Advances in Geometry 4 Algebraic & Geometric Topology 4 The Art of Discrete and Applied Mathematics 3 Journal of Mathematical Analysis and Applications 3 Journal of Mathematical Physics 3 Annales de l’Institut Fourier 3 Inventiones Mathematicae 3 Kodai Mathematical Journal 3 Osaka Journal of Mathematics 3 Siberian Mathematical Journal 3 Linear Algebra and its Applications 3 Expositiones Mathematicae 3 Journal of Algebraic Combinatorics 3 Mediterranean Journal of Mathematics 3 Bulletin of the American Mathematical Society 2 Bulletin of the Australian Mathematical Society 2 Periodica Mathematica Hungarica 2 Beiträge zur Algebra und Geometrie 2 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 2 Algebra and Logic 2 Bulletin of the London Mathematical Society 2 Journal of Approximation Theory 2 Journal of the Mathematical Society of Japan 2 Nagoya Mathematical Journal 2 Results in Mathematics 2 Combinatorica 2 Graphs and Combinatorics 2 International Journal of Algebra and Computation 2 Differential Geometry and its Applications 2 The Journal of Geometric Analysis 2 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 2 Journal de Théorie des Nombres de Bordeaux 2 Journal of Mathematical Sciences (New York) 2 St. Petersburg Mathematical Journal 2 The Electronic Journal of Combinatorics 2 Buletinul Academiei de Științe a Republicii Moldova. Matematica 2 Transformation Groups 2 Conformal Geometry and Dynamics 2 Journal of the Australian Mathematical Society 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Computational Methods and Function Theory 2 Kodai Mathematical Seminar Reports 2 Proceedings of the Steklov Institute of Mathematics 2 Groups, Geometry, and Dynamics 2 Albanian Journal of Mathematics 2 Ars Mathematica Contemporanea 1 Applicable Analysis 1 Communications on Pure and Applied Mathematics 1 Mathematics of Computation 1 Journal of Geometry and Physics 1 The Mathematical Intelligencer 1 Boletim da Sociedade Brasileira de Matemática 1 Bulletin de la Société Mathématique de France 1 Collectanea Mathematica 1 Commentarii Mathematici Helvetici 1 Compositio Mathematica 1 Computing 1 Indiana University Mathematics Journal 1 Journal of Functional Analysis 1 Journal of the London Mathematical Society. Second Series 1 Journal of Multivariate Analysis 1 Mathematica Slovaca ...and 61 more Serials all top 5 Cited in 46 Fields 199 Group theory and generalizations (20-XX) 181 Functions of a complex variable (30-XX) 121 Algebraic geometry (14-XX) 91 Convex and discrete geometry (52-XX) 90 Manifolds and cell complexes (57-XX) 76 Number theory (11-XX) 52 Combinatorics (05-XX) 39 Topological groups, Lie groups (22-XX) 21 Differential geometry (53-XX) 21 Probability theory and stochastic processes (60-XX) 19 Several complex variables and analytic spaces (32-XX) 16 Geometry (51-XX) 12 Real functions (26-XX) 10 Measure and integration (28-XX) 7 Linear and multilinear algebra; matrix theory (15-XX) 7 Abstract harmonic analysis (43-XX) 7 Global analysis, analysis on manifolds (58-XX) 6 Field theory and polynomials (12-XX) 6 Algebraic topology (55-XX) 6 Computer science (68-XX) 5 Associative rings and algebras (16-XX) 5 Difference and functional equations (39-XX) 5 Functional analysis (46-XX) 5 General topology (54-XX) 4 Special functions (33-XX) 3 History and biography (01-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 2 General and overarching topics; collections (00-XX) 2 General algebraic systems (08-XX) 2 \(K\)-theory (19-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Statistics (62-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Operations research, mathematical programming (90-XX) 2 Information and communication theory, circuits (94-XX) 1 Mathematical logic and foundations (03-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Commutative algebra (13-XX) 1 Nonassociative rings and algebras (17-XX) 1 Category theory; homological algebra (18-XX) 1 Partial differential equations (35-XX) 1 Approximations and expansions (41-XX) 1 Quantum theory (81-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Mathematics education (97-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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