On finite $p$-groups satisfying given laws
Group Theory
2018-10-24 v1
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 -groups in the given variety. Similarly, a variety contains only finitely many finite -groups of any given coclass if and only if not every group that is an extension of an abelian group by an elementary abelian -group belongs to that variety.
Cite
@article{arxiv.1810.09853,
title = {On finite $p$-groups satisfying given laws},
author = {Primoz Moravec},
journal= {arXiv preprint arXiv:1810.09853},
year = {2018}
}