Proceedings of the American Mathematical Society

The maximal normal $\,p$ -subgroup of the automorphism group of an abelian $\,p$ -group

Author(s): Jutta Hausen; Phillip Schultz
Journal: Proc. Amer. Math. Soc. 126 (1998), 2525-2533.
MSC (1991): Primary 20K10, 20F28, 20K30
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Abstract: Let

be a prime number and let $\,G\,$ be an abelian

-group. Let $\Delta$ be the maximal normal

-subgroup of $\operatorname{Aut}G$ and $\zeta$ the maximal

-subgroup of its centre. Let $\mathbf{t}$ be the torsion radical of ${\mathcal{E}}(G)$ . Then $\Delta =(1+\mathbf{t})\zeta$ . The result is new for

and 3, and the proof is new and valid for all primes

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Jutta Hausen
Affiliation: Department of Mathematics, University of Houston, Houston, Texas 77204-3476
Email: hausen@uh.edu

Phillip Schultz
Affiliation: Department of Mathematics, University of Western Australia, Nedlands 6009, Australia -
Email: schultz@maths.uwa.edu.au

DOI: 10.1090/S0002-9939-98-04496-7
PII: S 0002-9939(98)04496-7
Received by editor(s): January 28, 1997
Communicated by: Ronald M. Solomon
Copyright of article: Copyright 1998, American Mathematical Society

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