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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Near central automorphisms of abelian torsion groups


Author: Jutta Hausen
Journal: Trans. Amer. Math. Soc. 174 (1972), 199-215
MSC: Primary 20K10
MathSciNet review: 0310090
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0310090-X
PII: S 0002-9947(1972)0310090-X
Keywords: Abelian torsion group, automorphism, normal subgroups of automorphism groups, centralizers of subgroups of automorphism groups
Article copyright: © Copyright 1972 American Mathematical Society