On Inner Automorphisms of Finite Groups
Copyright policy )On Inner Automorphisms of Finite Groups
It is shown that in certain classes of finite groups, inner automorphisms are characterized by an extension property and also by a dual lifting property. This is a consequence of the fact that for any finite group G G and any prime p p , there is a p p -group P P and a semidirect product H = G P H = GP such that P P is characteristic in H H and every automorphism of H H induces an inner automorphism on H / P H/P .
Automorphisms of infinite groups, nilpotent \(\pi \) -groups, extendibility property, Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure, solvable \(\pi \) -groups, inner automorphisms, special p-subgroup, Automorphisms of abstract finite groups
Automorphisms of infinite groups, nilpotent \(\pi \) -groups, extendibility property, Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure, solvable \(\pi \) -groups, inner automorphisms, special p-subgroup, Automorphisms of abstract finite groups
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