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FINITE $p$-GROUPS ALL OF WHOSE NONNORMAL SUBGROUPS HAVE BOUNDED NORMAL CORES
Published online by Cambridge University Press: 18 July 2019
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.
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- Research Article
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- Copyright
- © 2019 Australian Mathematical Publishing Association Inc.
Footnotes
This work was supported by the National Natural Science Foundation of China (11671324, 11471266).
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