Abstract
Let G be a finite group. An automorphism \(\alpha \) of G is called an \(\text{ IA }\) automorphism if it induces the identity automorphism on the abelianized group \(G/G'\). Let \(\text{ IA }(G)\) be the group of all \(\text{ IA }\) automorphisms of G, and let \(\text{ IA }(G)^*\) be the group of all \(\text{ IA }\) automorphisms of G which fix Z(G) element-wise. Let \(\mathrm {Var}(G)\) be the group of all autocentral automorphisms of G. We find necessary and sufficient conditions for a finite p-group G such that \(\text{ IA }(G)^*=\text{ Var }(G)\). We also extend the famous result of Adney and Yen (Theorem 1 of Ill J Math 9:137–143, 1965).
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Acknowledgements
The authors are thankful to the reviewers for their useful comments and suggestions. Research of second author is supported by SERB, DST Grant No. MTR/2019/000220. Research of third author is supported by SERB, DST Grant No. MTR/2017/000581.
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Chahal, S.S., Gumber, D. & Kalra, H. On Autocentral Automorphisms of Finite p-Groups. Results Math 76, 30 (2021). https://doi.org/10.1007/s00025-020-01336-8
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DOI: https://doi.org/10.1007/s00025-020-01336-8