On groups with a central automorphism of infinite order

Dixon, Martyn R.; Evans, M. J.

doi:10.1090/S0002-9939-1992-1072334-7

On groups with a central automorphism of infinite order
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by Martyn R. Dixon and M. J. Evans PDF

Proc. Amer. Math. Soc. 114 (1992), 331-336 Request permission

Abstract:

It is shown that a group $G$, whose center has finite exponent, has a central automorphism of infinite order if and only if $G$ has an infinite abelian direct factor. It is also shown that the group of central automorphisms of a nilpotent $p$-group of infinite exponent contains an uncountable torsionfree abelian subgroup

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A nilpotent

-group has an outer automorphism

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