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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Finite groups with semisimple endomorphism rings


Author: Carter Lyons
Journal: Proc. Amer. Math. Soc. 53 (1975), 51-52
MSC: Primary 16A76
DOI: https://doi.org/10.1090/S0002-9939-1975-0382364-6
MathSciNet review: 0382364
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Abstract: If the near ring $ E(G)$ generated by the endomorphisms of a finite group $ G$ is a semisimple ring, or more generally, has square-free characteristic then it is shown that $ G$ is abelian, a direct sum of elementary $ p$-groups.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0382364-6
Keywords: Endomorphism near ring, finite group, nilpotent group, Sylow $ p$-subgroup, elementary abelian $ p$-group, solvable group, fully invariant subgroup
Article copyright: © Copyright 1975 American Mathematical Society