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A NOTE ON NORMAL COMPLEMENTS FOR FINITE GROUPS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 98 / Issue 1 / August 2018
- Published online by Cambridge University Press:
- 29 April 2018, pp. 109-112
- Print publication:
- August 2018
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- Article
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- You have access
- Export citation
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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 
$H\cap N=1$.
