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ON THE CENTRAL KERNEL OF A GROUP
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 108 / Issue 2 / October 2023
- Published online by Cambridge University Press:
- 13 October 2022, pp. 283-289
- Print publication:
- October 2023
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- Article
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The central kernel
$K(G)$ of a group G is the (characteristic) subgroup consisting of all elements 
$x\in G$ such that 
$x^{\gamma }=x$ for every central automorphism 
$\gamma $ of G. We prove that if G is a finite-by-nilpotent group whose central kernel has finite index, then the full automorphism group 
$Aut(G)$ of G is finite. Some applications of this result are given.
