Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Minimal presentations for certain metabelian groups

Authors: D. G. Searby and J. W. Wamsley
Journal: Proc. Amer. Math. Soc. 32 (1972), 342-348
MSC: Primary 20E05
MathSciNet review: 0291263
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let G be a finite p-group, $ d(G) = \dim {H^1}(G,Z/pZ)$ and $ r(G) = \dim {H^2}(G,Z/pZ)$. Then $ d(G)$ is the minimal number of generators of G, and we say that G is a member of a class $ {\mathcal{G}_p}$ of finite p-groups if G has a presentation with $ d(G)$ generators and $ r(G)$ relations. The main result is that any outer extension of a finite cyclic p-group by a finite abelian p-group belongs to $ {\mathcal{G}_p}$.

References [Enhancements On Off] (What's this?)

  • [1] D. Epstein, Finite presentations of groups and 3-manifolds, Quart. J. Math. Oxford Ser. (2) 12 (1961), 205-212. MR 26 #1867. MR 0144321 (26:1867)
  • [2] J.-P. Serre, Cohomologie galoisienne, 3rd ed., Lecture Notes in Math., no. 5, Springer-Verlag, Berlin and New York, 1965. MR 34 #1328. MR 0201444 (34:1328)
  • [3] J. W. Wamsley, The deficiency of metacyclic groups, Proc. Amer. Math. Soc. 24 (1970), 724-726. MR 41 #3576. MR 0258931 (41:3576)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20E05

Retrieve articles in all journals with MSC: 20E05

Additional Information

Keywords: Presentation, outer extension, finite cyclic p-group, finite abelian p-group, Frattini subgroup
Article copyright: © Copyright 1972 American Mathematical Society

American Mathematical Society