$۴$-quasinormal subgroups of prime order
Publish place: International Journal of Group Theory، Vol: 9، Issue: 1
Publish Year: 1399
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_THEGR-9-1_004
تاریخ نمایه سازی: 14 اردیبهشت 1400
Abstract:
Generalizing the concept of quasinormality, a subgroup $H$ of a group $G$ is said to be ۴-quasinormal in $G$ if, for all cyclic subgroups $K$ of $G$, $\langle H,K\rangle=HKHK$. An intermediate concept would be ۳-quasinormality, but in finite $p$-groups - our main concern - this is equivalent to quasinormality. Quasinormal subgroups have many interesting properties and it has been shown that some of them can be extended to ۴-quasinormal subgroups, particularly in finite $p$-groups. However, even in the smallest case, when $H$ is a ۴-quasinormal subgroup of order $p$ in a finite $p$-group $G$, precisely how $H$ is embedded in $G$ is not immediately obvious. Here we consider one of these questions regarding the commutator subgroup $[H,G]$.
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Authors
Stewart Stonehewer
University of Warwick