On finite $p$-groups satisfying given laws

Primoz Moravec

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arXiv · 1810.09853

On finite $p$-groups satisfying given laws

Primoz Moravec

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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.

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Primoz Moravec. 2018-10-23. On finite $p$-groups satisfying given laws. https://arxiv.org/abs/1810.09853

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