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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On a theorem of Deskins


Author: Irene Zimmermann
Journal: Proc. Amer. Math. Soc. 107 (1989), 895-899
MSC: Primary 20D10; Secondary 20D30
MathSciNet review: 986654
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Abstract: In this note we present a solvability criterion for finite groups. We show that a finite group $ G$ is solvable if in every maximal subgroup chain of length 3 of $ G$ at least one term is a submodular subgroup of $ G$. This generalizes an earlier result of Deskins.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0986654-5
PII: S 0002-9939(1989)0986654-5
Article copyright: © Copyright 1989 American Mathematical Society