Is there a standard term to denote finite groups $G$ with the property that the projection $\operatorname{Aut} G \to \operatorname{Out} G$ from automorphisms of $G$ to outer automorphisms is split?
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1$\begingroup$ The finite simple groups with this property are characterised in this paper. See also this question, which I just noticed. $\endgroup$– Carl-Fredrik Nyberg BroddaCommented Aug 3, 2022 at 16:38
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1$\begingroup$ Name of the paper referenced by @Carl-FredrikNybergBrodda: Lucchini, Menegazzo, and Morigi - On the existence of a complement for a finite simple group in its automorphism group; title of the question referenced in the same comment: Non-split Aut(G) $\to$ Out(G)? $\endgroup$– LSpiceCommented Aug 3, 2022 at 18:05
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$\begingroup$ In fact this property makes perfect sense for all groups, finite infinite. $\endgroup$– Derek HoltCommented Aug 3, 2022 at 18:11
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$\begingroup$ Thanks a lot. So, it appears that the is no standard name; but the paper by Lucchini, Menegazzo and Morigi is very interesting. $\endgroup$– AngeloCommented Aug 4, 2022 at 10:10
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