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The maximal normal -group
Authors:Jutta Hausen   Phillip Schultz
Affiliation:Department of Mathematics, University of Houston, Houston, Texas 77204-3476 ; Department of Mathematics, University of Western Australia, Nedlands 6009, Australia -
Abstract:Let $p$ be a prime number and let $,G,$ be an abelian $p$-group. Let $Delta $ be the maximal normal $p$-subgroup of $operatorname{Aut}G$ and $zeta $ the maximal $p$-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 $p=2$ and 3, and the proof is new and valid for all primes $p$.

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