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FINITE
$p$-GROUPS ALL OF WHOSE NONNORMAL SUBGROUPS HAVE BOUNDED NORMAL CORES
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 101 / Issue 2 / April 2020
- Published online by Cambridge University Press:
- 18 July 2019, pp. 255-265
- Print publication:
- April 2020
-
- Article
- Export citation
-
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.
