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The Influence on a Finite Group of its Permutable Subgroups
Published online by Cambridge University Press: 20 November 2018
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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.
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- Copyright © Canadian Mathematical Society 1974
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