A NOTE ON NORMAL COMPLEMENTS FOR FINITE GROUPS

A NOTE ON NORMAL COMPLEMENTS FOR FINITE GROUPS

Assume that $G$ is a finite group and $H$ is a 2-nilpotent Sylow tower Hall subgroup of $G$ such that if $x$ and $y$ are $G$ -conjugate elements of $H\cap G^{\prime }$ of prime order or order 4, then $x$ and $y$ are $H$ -conjugate. We prove that there exists a normal subgroup $N$ of $G$ such that $G...

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Veröffentlicht in:Bulletin of the Australian Mathematical Society 2018-08, Vol.98 (1), p.109-112
Hauptverfasser: SU, NING, BALLESTER-BOLINCHES, ADOLFO, MENG, HANGYANG
Format: Artikel
Sprache:eng
Schlagworte:
Conjugates
Hypotheses
Subgroups
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Beschreibung
Zusammenfassung:Assume that $G$ is a finite group and $H$ is a 2-nilpotent Sylow tower Hall subgroup of $G$ such that if $x$ and $y$ are $G$ -conjugate elements of $H\cap G^{\prime }$ of prime order or order 4, then $x$ and $y$ are $H$ -conjugate. We prove that there exists a normal subgroup $N$ of $G$ such that $G=HN$ and $H\cap N=1$ .
ISSN:0004-9727
1755-1633
DOI:10.1017/S0004972718000151