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Classification of soluble groups of cohomological dimension two. (English) Zbl 0414.20032

MSC:
20F16 Solvable groups, supersolvable groups
20J05 Homological methods in group theory
20F05 Generators, relations, and presentations of groups
20E34 General structure theorems for groups
20E07 Subgroup theorems; subgroup growth
18G20 Homological dimension (category-theoretic aspects)
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References:
[1] Baer, R., Heineken, H.: Radical groups of finite abelian subgroup rank. Illinois J. Math.16, 533-580 (1972) · Zbl 0248.20052
[2] Baumslag, G., Strebel, R.: Some finitely generated, infinitely related metabelian groups with trivial multiplicator. J. Algebra40, 46-62 (1976) · Zbl 0353.20037
[3] Bieri, R.: Homological Dimension of Discrete Groups. Queen Mary College Mathematics Notes. London El: Queen Mary College (University of London) 1976 · Zbl 0357.20027
[4] Bieri, R.: Über die cohomologische Dimension der Auflösbaren Gruppen. Math. Z.128, 235-243 (1972) · Zbl 0237.20027
[5] Bieri, R., Strebel, R.: Almost finitely presented soluble groups. Comment. Math. Helv.53, 258-278 (1978) · Zbl 0373.20035
[6] ?arin, V.S.: On soluble groups of typeA 4. Mat. Sb.52, (94), 895-914 (1960)
[7] Connell, I.: On the group ring. Canad. J. Math.15, 650-685 (1963) · Zbl 0121.03502
[8] Fel’dman, G.: On the homological dimension of group algebras of solvable groups (Russian). Izv. Akad. Nauk SSSR Ser. Mat.35, 1225-1236 (1971). Translated in: Math. USSR-Izv. 5, 2, 1231-1244 (1971) · Zbl 0234.18008
[9] Gruenberg, K.: Cohomological Topics in Group Theory. Lecture Notes in Mathematics143. Berlin-Heidelberg-New York: Springer 1970 · Zbl 0205.32701
[10] Plotkin, B.Z.: Radical Groups. Amer. Math. Soc. Transl. (2)17, 9-28 (1961) · Zbl 0128.25402
[11] Serre, J.-P.: Cohomologie des Groupes Discrets. In: Hirzebruch, F. et al.: Prospects in Mathematics. Annals of Mathematics Studies70, pp. 77-169. Princeton, N.J.: Princeton University Press 1971
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