Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On automorphism groups and endomorphism rings of abelian $ p$-groups

Author: Jutta Hausen
Journal: Trans. Amer. Math. Soc. 210 (1975), 123-128
MSC: Primary 20K30
MathSciNet review: 0376906
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ A$ be a noncyclic abelian $ p$-group where $ p \geqslant 5$, and let $ {p^\infty }A$ be the maximal divisible subgroup of $ A$. It is shown that $ A/{p^\infty }A$ is bounded and nonzero if and only if the automorphism group of $ A$ contains a minimal noncentral normal subgroup. This leads to the following connection between the ideal structure of certain rings and the normal structure of their groups of units: if the noncommutative ring $ R$ is isomorphic to the full ring of endomorphisms of an abelian $ p$-group, $ p \geqslant 5$, then $ R$ contains minimal twosided ideals if and only if the group of units of $ R$ contains minimal noncentral normal subgroups.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 20K30

Retrieve articles in all journals with MSC: 20K30

Additional Information

Keywords: Abelian $ p$-group, automorphism group, normal subgroups of automorphism groups, endomorphism ring
Article copyright: © Copyright 1975 American Mathematical Society

American Mathematical Society