On finite p-groups satisfying given laws

2018/10/23 by Moravec, Primoz
#20D15 #20E10 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1810.09853

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.

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