TY - JOUR
ID - 27183
TI - The influence of $\mathscr{H}$-subgroups on $p$-nilpotency and $p$-supersolvability of finite groups
JO - International Journal of Group Theory
JA - IJGT
LA - en
SN - 2251-7650
AU - Yan, Quanfu
AU - Shen, Zhencai
AD - Department of Mathematical Sciences, Kent State University, Kent, USA
AD - Department of Mathematics, College of Science, China Agricultural University, Beijing, China.
Y1 - 2024
PY - 2024
VL - 13
IS - 1
SP - 55
EP - 62
KW - $\mathscr{H}$-subgroup
KW - weakly $\mathscr{H}$-subgroup
KW - $p$-supersolvablility
KW - $p$-nilpotency
DO - 10.22108/ijgt.2023.135208.1806
N2 - Let $G$ be a finite group. A subgroup $H$ of $G$ is an $\mathscr{H}$-subgroup in $G$ if $N_G(H)\cap H^g \leq H$ for any $g \in G$. In this article, by using the concept of $\mathscr{H}$-subgroups, we study the influence of the intersection of $O^p(G_p^*)$ and the members of some fixed $\mathcal{M}_d(P)$ on the structure of the group $G$, where $P$ is a Sylow $p$-subgroup of $G.$ Some new criteria for a group to be $p$-nilpotent and $p$-supersolvable are given and some recent results are extended and generalized.
UR - https://ijgt.ui.ac.ir/article_27183.html
L1 - https://ijgt.ui.ac.ir/article_27183_6122c42af4f745fb4589174b1fb7e93b.pdf
ER -