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 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.
