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Minimal presentations for certain group extensions

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Abstract

IfG is a finite group thend(G) denotes the minimal number of generators ofG. IfH andK are groups then the extension, 1 →H →G →K → 1, is called an outer extension ofK byH ifd(G)=d(H)+d(K). Let

be the class of groups containing all finitep-groupsG which has a presentation withd(G) = dimH 1(G,z p ) generators andr(G)=dimH 2 (G,Z p ) relations: in this article it is shown that ifK is a non cyclic group belonging to

andH is a finite abelian p-group then any outer extension ofK byH belongs to

.

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References

  1. R. C. Lyndon,The cohomology theory of group extensions, Duke Math, J.15 (1948), 271–292.

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Authors and Affiliations

  1. School of Mathematical Sciences, The Flinders University of South Australia, Australia

    J. W. Wamsley

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  1. J. W. Wamsley
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Wamsley, J.W. Minimal presentations for certain group extensions. Israel J. Math. 9, 459–463 (1971). https://doi.org/10.1007/BF02771460

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  • DOI: https://doi.org/10.1007/BF02771460

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