Search results for "Sporadic group"

showing 3 items of 3 documents

On đť“•-subnormal subgroups and Frattini-like subgroups of a finite group

1994

Throughout the paper we consider only finite groups.J. C. Beidleman and H. Smith [3] have proposed the following question: “If G is a group and Ha subnormal subgroup of G containing Φ(G), the Frattini subgroup of G, such that H/Φ(G)is supersoluble, is H necessarily supersoluble? “In this paper, we give not only an affirmative answer to this question but also we see that the above result still holds if supersoluble is replaced by any saturated formation containing the class of all nilpotent groups.

CombinatoricsSubnormal subgroupNilpotentClass (set theory)Finite groupGroup (mathematics)Locally finite groupGeneral MathematicsFrattini subgroupSporadic groupMathematicsGlasgow Mathematical Journal
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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)Ă€lgebraMATEMATICA APLICADAMathematics::Representation TheoryMathematicsAnnali di Matematica Pura ed Applicata (1923 -)
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On minimal subgroups of finite groups

1996

Pure mathematicsGroup of Lie typeLocally finite groupGeneral MathematicsSporadic groupMathematicsZ-group
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