M. J. Curran
Abstract
For any group G, the centre of the inner automorphism group, Z(Inn(G)) is always contained in the group Autc (G) of central automorphisms of G. In this paper we consider finite groups for which this lower bound is attained, that is Autc (G) = Z(Inn(G)), and give a characterisation of such groups.
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For any group G, the centre of the inner automorphism group, Z(Inn(G)) is always contained in the group Autc (G) of central automorphisms of G. In this paper we consider finite groups for which this lower bound is attained, that is Autc (G) = Z(Inn(G)), and give a characterisation of such groups.
Key concepts: Order (exchange), Group (periodic table), Mathematics, Automorphism, Inner automorphism, Outer automorphism group, p-group, Automorphism group