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2012•Università del SalentoOpen access

Autocommutator subgroups with cyclic outer automorphism group

Mohammad Naghshineh, Mohammad Farrokhi Derakhshandeh Ghouchan, Mohammad Reza R. Moghaddam

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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.

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What this paper is about

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.

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Available 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.

Key concepts: Outer automorphism group, Inner automorphism, Mathematics, Alternating group, Automorphism, p-group, Cyclic group, Group (periodic table)

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