On finite p-groups satisfying given laws

被引：0

作者：

Moravec, Primoz ^{[1
]}

机构：

[1] Univ Ljubljana, Fac Math & Phys, Ljubljana, Slovenia

来源：

MONATSHEFTE FUR MATHEMATIK | 2019年 / 190卷 / 03期

关键词：

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

D O I：

10.1007/s00605-018-1250-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：589 / 593

页数：5

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