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- Title
FINITE $p$ -GROUPS ALL OF WHOSE NONNORMAL SUBGROUPS HAVE BOUNDED NORMAL CORES.
- Authors
YANG, DONGFANG; AN, LIJIAN; LV, HENG
- Abstract
Given a positive integer $m$ , a finite $p$ -group $G$ is called a $BC(p^{m})$ -group if $|H_{G}|\leq p^{m}$ for every nonnormal subgroup $H$ of $G$ , where $H_{G}$ is the normal core of $H$ in $G$. We show that $m+2$ is an upper bound for the nilpotent class of a finite $BC(p^{m})$ -group and obtain a necessary and sufficient condition for a $p$ -group to be of maximal class. We also classify the $BC(p)$ -groups.
- Subjects
NILPOTENT groups; INTEGERS; FINITE, The; SUBGROUP growth
- Publication
Bulletin of the Australian Mathematical Society, 2020, Vol 101, Issue 2, p255
- ISSN
0004-9727
- Publication type
Article
- DOI
10.1017/S0004972719000753