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ON THE CENTRAL KERNEL OF A GROUP

Part of: Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  13 October 2022

ALESSIO RUSSO Open the ORCID record for ALESSIO RUSSO [Opens in a new window]
ALESSIO RUSSO*
Affiliation:
Dipartimento di Matematica e Fisica, Università della Campania ‘Luigi Vanvitelli’, Viale Lincoln 5, Caserta, Italy
*
e-mail: alessio.russo@unicampania.it
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Abstract

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.

Keywords

central automorphismcentral kernel

MSC classification

Primary: 20E36: Automorphisms of infinite groups
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 108 , Issue 2 , October 2023 , pp. 283 - 289
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

The author is a member of GNSAGA-INdAM and ADV-AGTA. This work was carried out within the ‘VALERE: VAnviteLli pEr la RicErca’ project.

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