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On commuting automorphisms of finite groups

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Abstract

Let G be a group. An automorphism \(\alpha \) of G is called a commuting automorphism if \(\alpha (x)x= x \alpha (x)\) for all \(x \in G\). The set of all commuting automorphisms of G is denoted by A(G). The set A(G) does not necessarily form a subgroup of the automorphism group of G. If A(G) form a subgroup, then we say G is an A-group. In this paper, we show that the direct product of two finite A-groups is also an A-group. We also show that GL(nq) for \(n = 3\) or \(q >n\), PSL(2, q) and ZM-groups are A-groups.

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Correspondence to Pradeep Kumar.

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Communicated by F. Degiovanni.

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Kumar, P. On commuting automorphisms of finite groups. Ricerche mat 68, 899–904 (2019). https://doi.org/10.1007/s11587-019-00444-0

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  • DOI: https://doi.org/10.1007/s11587-019-00444-0

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