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LOCALLY FINITE GROUPS WHOSE SUBGROUPS HAVE FINITE NORMAL OSCILLATION
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 89 / Issue 3 / June 2014
- Published online by Cambridge University Press:
- 20 November 2013, pp. 479-487
- Print publication:
- June 2014
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- Article
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- You have access
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If
$X$ is a subgroup of a group 
$G$, the cardinal number 
$\min \{ \vert X: X_{G}\vert , \vert {X}^{G} : X\vert \} $ is called the normal oscillation of 
$X$ in 
$G$. It is proved that if all subgroups of a locally finite group 
$G$ have finite normal oscillation, then 
$G$ contains a nilpotent subgroup of finite index.
