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On finite p-groups satisfying given laws

  • Primož MoravecEmail author
Article
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Abstract

A variety of groups does not contain all metabelian groups if and only if there is an absolute bound for the nilpotency classes of powerful p-groups in the given variety. Similarly, a variety contains only finitely many finite p-groups of any given coclass if and only if not every group that is an extension of an abelian group by an elementary abelian p-group belongs to that variety.

Keywords

Finite p-groups Varieties of groups Coclass Powerful p-groups 

Mathematics Subject Classification

20D15 20E10 

Notes

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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of Mathematics and PhysicsUniversity of LjubljanaLjubljanaSlovenia

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