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The Influence on a Finite Group of its Permutable Subgroups

Published online by Cambridge University Press:  20 November 2018

Ram K. Agrawal
Ram K. Agrawal*
Affiliation:
Ferris State College, Big Rapids, Michigan
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Huppert, Janko and Mann have proved the following theorems for a finite group G.

(Huppert [4]). If each second maximal subgroup of G is normal in G, then G is supersolvable. If the order of G is divisible by at least three different primes, then G is nilpotent.

(Huppert [4]). Let each third maximal subgroup of G be normal in G. Then: (i) G′ is nilpotent; (ii) the rank of G=r(G)≤2; (iii) if |G| is divisible by at least three different primes, then G is supersolvable.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 2 , 01 June 1974 , pp. 159 - 165
Copyright
Copyright © Canadian Mathematical Society 1974

References

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