Search results for "Maximal subgroups"

showing 2 items of 2 documents

Maximal subgroups and PST-groups

2013

A subgroup H of a group G is said r to permute with a subgroup K of G if HK is a subgroup of G. H is said to be permutable (resp. S-permutable) if it permutes with all the subgroups (resp. Sylow subgroups) of G. Finite groups in which permutability (resp. S-permutability) is a transitive relation are called PT-groups (resp. PST-groups). PT-, PST- and T-groups, or groups in which normality is transitive, have been extensively studied and characterised. Kaplan [Kaplan G., On T-groups, supersolvable groups, and maxmial subgroups, Arch. Math. (Basel), 2011, 96(1), 19-25)] presented some new characterisations of soluble T-groups. The main goal of this paper is to establish PT- and PST-versions o…

20e2820d05General MathematicsCombinatoricsLocally finite groupPermutabilityQA1-939Permutable prime20d10Algebra over a fieldMathematicsDiscrete mathematicsTransitive relation20f16Group (mathematics)20e15Sylow theoremsGrups Teoria deSylow-permutabilitySupersolubilityFinite groupsNumber theoryMaximal subgroupsÀlgebraMATEMATICA APLICADAMathematics
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On a class of generalised Schmidt groups

2015

In this paper families of non-nilpotent subgroups covering the non-nilpotent part of a finite group are considered. An A 5 -free group possessing one of these families is soluble, and soluble groups with this property have Fitting length at most three. A bound on the number of primes dividing the order of the group is also obtained.

Group (mathematics)Applied MathematicsMathematics::Rings and AlgebrasGrups Teoria deCycle graph (algebra)Sporadic groupFinite groupsNon-abelian groupCombinatoricsMathematics::Group TheoryGroup of Lie typeLocally finite groupSimple groupNilpotent groupsMaximal subgroupsOrder (group theory)ÀlgebraMATEMATICA APLICADAMathematics::Representation TheoryMathematicsAnnali di Matematica Pura ed Applicata (1923 -)
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