Conway, John H.; Hulpke, Alexander; McKay, John On transitive permutation groups. (English) Zbl 0920.20001 LMS J. Comput. Math. 1, 1-8, Appendix A 38 p., Appendix B (1998). This paper presents a scheme for giving meaningful names to permutation groups, based partly on the subnormal structure (as in ATLAS notation) but also considering the permutation structure. This is applied to all of the (previously classified) transitive permutation groups of degree up to 15.In a lengthy appendix all these groups are listed, giving for each group not only the name but also explicit generators (chosen to reflect the structure) and some other information about the group’s properties. The tables were created in a largely automated way, using GAP, to reduce errors and provide a check on the correctness of the list. Reviewer: A.J.Goodman (Rolla) Cited in 3 ReviewsCited in 34 Documents MSC: 20B35 Subgroups of symmetric groups 20B20 Multiply transitive finite groups 20B40 Computational methods (permutation groups) (MSC2010) Keywords:transitive permutation groups; names; generators PDFBibTeX XMLCite \textit{J. H. Conway} et al., LMS J. Comput. Math. 1, 1--8, Appendix A 38\,p., Appendix B (1998; Zbl 0920.20001) Full Text: DOI Link Online Encyclopedia of Integer Sequences: Number of transitive permutation groups of degree n. References: [1] Burckhardt, Encyclopädie der mathematischen Wissenschaften (1898) [2] DOI: 10.1080/00927878308822884 · Zbl 0518.20003 [3] C. R. Acad. Sci. Paris pp 793– (1857) [4] Short, The primitive soluble permutation groups of degree less than 256 (1992) · Zbl 0752.20001 [5] DOI: 10.1016/S0747-7171(87)80068-8 · Zbl 0683.20002 [6] Remak, J. Reine Angew. Math 163 pp 1– (1930) [7] DOI: 10.1006/jsco.1993.1056 · Zbl 0813.20003 [8] Miller, Quart. J. Pure Appl. Math 29 pp 224– (1898) [9] DOI: 10.2307/2369906 · JFM 35.0172.01 [10] Miller, Quart. J. Pure Appl. Math. 28 pp 193– (1896) [11] Krasner, Acta Sci. Math. (Szeged) 14 pp 39– (1951) [12] Cannon, An introduction to Magma (1993) [13] Conway, ATLAS of finite groups (1985) [14] Miller, The Collected Works of George Abram Miller 1 (1935) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.