Near central automorphisms of abelian torsion groups

Hausen, Jutta

doi:10.1090/S0002-9947-1972-0310090-X

Near central automorphisms of abelian torsion groups
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Trans. Amer. Math. Soc. 174 (1972), 199-215 Request permission

Abstract:

This paper is concerned with the normal structure of the automorphism group $A(T)$ of an abelian torsion group T. The concept of the near center of a group is introduced in order to determine all subgroups of $A(T)$ the centralizer of which has finite index. Consequences are the fact that the finite normal subgroups of $A(T)$ are nilpotent if T is a primary group of infinite rank, and that every normal torsion subgroup of $A(T)$ is contained in the center of $A(T)$ if T is divisible.

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