Autocommutator subgroups with cyclic outer automorphism group


Abstract


A criterion for the existence of groups admitting autocommutator subgroups with cyclic outer automorphism group is given. Also the classification of those finite groups G such that K(G)\cong H if H is a centerless finite group with cyclic outer automorphism group and possible solutions G if |Z(H)|=2 and H has a cyclic outer automorphism group is presented.

DOI Code: 10.1285/i15900932v31n2p9

Keywords: Autocommutator subgroup ; outer automorphism

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