On finite insoluble groups with nilpotent maximal subgroups

Rose, John S.

doi:10.1016/0021-8693(77)90301-5

Cited by 52 publications

(11 citation statements)

References 17 publications

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“…Thus D 1 /F G is a maximal and nilpotent subgroup of a nonabelian simple group G/F G . Applying Rose's result (see [12]), we get that…”

Section: Claim 6 Finial Contradictionmentioning

confidence: 94%

Finite Groups withS-permutablen-maximal Subgroups

Qian

2015

Communications in Algebra

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Let G be a finite group and M n G be the set of n-maximal subgroups of G, where n is an arbitrary given positive integer. Suppose that M n G contains a nonidentity member and all members in M n G are S-permutable in G. Then any of of the following conditions guarantees the supersolvability of G: (1) M n G contains a nonidentity member whose order is not a prime; (2) all nonidentity members in M n G are of prime order, and all cyclic members in M n−1 G of order 4 are S-permutable in G.

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“…Thus D 1 /F G is a maximal and nilpotent subgroup of a nonabelian simple group G/F G . Applying Rose's result (see [12]), we get that…”

Section: Claim 6 Finial Contradictionmentioning

confidence: 94%

Finite Groups withS-permutablen-maximal Subgroups

Qian

2015

Communications in Algebra

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“…Let G be a minimal counterexample and let M 2 be the normal 2-complement of M . Then M 2 is normal in G by [15,Theorem 1]. It is clear that G/M 2 satisfies the hypotheses of the theorem.…”

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confidence: 88%

THE $c$-SUPPLEMENTED PROPERTY OF FINITE GROUPS

Wei

Wang²

2007

Proceedings of the Edinburgh Mathematical Society

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“…Since Z(G) = 1, one has that all nilpotent maximal subgroups of G are Sylow 2subgroups of G by [6,Theorem1]. Then the maximal subgroups of G may only be: Sylow 2-subgroups, non-nilpotent maximal subgroups of order divisible by p or non-nilpotent maximal subgroups of p ′ -order.…”

Section: Proof Of Theorem 13mentioning

confidence: 99%

“…(ii) Suppose Z(G) = 1. By [6,Theorem1], every nilpotent maximal of G is a Sylow 2-subgroup of G. It implies that P cannot be contained in any nilpotent maximal subgroup of G since p > 2, this contradicts that P can only be contained in a nilpotent maximal subgroup of G.…”

Section: Introductionmentioning

confidence: 99%