Non-nilpotent subgroups of locally graded groups
Volume 138 / 2015
Colloquium Mathematicum 138 (2015), 145-148
MSC: Primary 20E99.
DOI: 10.4064/cm138-1-9
Abstract
We show that a locally graded group with a finite number $m$ of non-(nilpotent of class at most $n$) subgroups is (soluble of class at most $[\log_2n]+m+3$)-by-(finite of order $\leq m!$). We also show that the derived length of a soluble group with a finite number $m$ of non-(nilpotent of class at most $n$) subgroups is at most $[\log_2 n]+m+1$.
