A remark on generalized covering groups

zbMATH Open0918.20015arXiv1104.0397MaRDI QIDQ1276487

Behrooz Mashayekhy

Publication date: 16 August 1999

Published in: Indian Journal of Pure \& Applied Mathematics (Search for Journal in Brave)

Abstract: Let ${calN}_c$ be the variety of nilpotent groups of class at most $c(cgeq2)$ and $G=Z_{r}oplus{Z}_s$ be the direct sum of two finite cyclic groups. It is shown that if the greatest common divisor of $r$ and $s$ is not one, then $G$ does not have any ${calN}_c$-covering group for every $cgeq2$. This result gives an idea that Lemma 2 of J.Wiegold [6] and Haebich's Theorem [1], a vast generalization of the Wiegold's Theorem, can {it not} be generalized to the variety of nilpotent groups of class at most $cgeq2$.

Full work available at URL: https://arxiv.org/abs/1104.0397

zbMATH Keywords

Baer invariantsvarieties of nilpotent groupslower central seriesbasic commutators

Mathematics Subject Classification ID

Nilpotent groups (20F18) Quasivarieties and varieties of groups (20E10)

This page was built for publication: A remark on generalized covering groups