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Title

‎$‎۴‎$‎-quasinormal subgroups of prime order

Year: 1399
COI: JR_THEGR-9-1_004
Language: EnglishView: 17
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Authors

Stewart Stonehewer - University of Warwick

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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This Paper COI Code is JR_THEGR-9-1_004. Also You can use the following address to link to this article. This link is permanent and is used as an article registration confirmation in the Civilica reference:

https://civilica.com/doc/1194938/

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Stonehewer, Stewart,1399,‎$‎۴‎$‎-quasinormal subgroups of prime order,https://civilica.com/doc/1194938

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