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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
DOI: https://doi.org/10.1090/S0002-9939-1972-0291263-7
MathSciNet review: 0291263
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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}$.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0291263-7
Keywords: Presentation, outer extension, finite cyclic p-group, finite abelian p-group, Frattini subgroup
Article copyright: © Copyright 1972 American Mathematical Society