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

Complete groups with nonabelian composition factors


Author: Jay Zimmerman
Journal: Trans. Amer. Math. Soc. 302 (1987), 151-159
MSC: Primary 20B35; Secondary 20F28
MathSciNet review: 887502
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Abstract: A finite group is said to be complete if it has trivial center and if every automorphism is an inner automorphism. A finite group with nonabelian composition factors has a unique completely reducible radical (CR radical). We consider finite groups with nonabelian composition factors whose CR radical consists of complete simple groups and we give necessary and sufficient conditions for such a group to be complete. This involves finding group theoretic conditions which are necessary and sufficient for a finite centerless group to occur as a self-normalizing subgroup of a direct product of symmetric groups.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1987-0887502-7
PII: S 0002-9947(1987)0887502-7
Keywords: Complete group, permutation group, symmetric group
Article copyright: © Copyright 1987 American Mathematical Society