Search results for "Permutability"

showing 4 items of 14 documents

Sylow permutable subnormal subgroups of finite groups II

2001

[EN] In this paper a local version of Agrawal's theorem about the structure of finite groups in which Sylow permutability is transitive is given. The result is used to obtain new characterisations of this class of finite groups.

Permutability conditionsTransitive relationClass (set theory)Soluble groupGeneral MathematicsSubnormal p'-perfect subgroupSylow theoremsStructure (category theory)Grups Teoria dePst_p-groupHall subgroupsCombinatoricsLocally finite groupComponent (group theory)ÀlgebraPermutable primeAlgebra over a fieldMathematicsBulletin of the Australian Mathematical Society
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On finite soluble groups in which Sylow permutability is a transitive relation

2003

A characterisation of finite soluble groups in which Sylow permutability is a transitive relation by means of subgroup embedding properties enjoyed by all the subgroups is proved in the paper. The key point is an extension of a subnormality criterion due to Wielandt.

Finite groupTransitive relationGeneral MathematicsSylow theoremsGrups Teoria deExtension (predicate logic)CombinatoricsMathematics::Group TheoryKey pointLocally finite groupPermutabilitySubnormalityEmbeddingÀlgebraFinite groupAlgebra over a fieldMATEMATICA APLICADAMathematicsActa Mathematica Hungarica
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On some classes of supersoluble groups

2007

[EN] Finite groups G for which for every subgroup H and for all primes q dividing the index |G:H| there exists a subgroup K of G such that H is contained in K and |K:H|=q are called Y-groups. Groups in which subnormal subgroups permute with all Sylow subgroups are called PST-groups. In this paper a local version of the Y-property leading to a local characterisation of Y-groups, from which the classical characterisation emerges, is introduced. The relationship between PST-groups and Y-groups is also analysed.

p-groupNormal subgroupDiscrete mathematicsComplement (group theory)Lagrange theoremAlgebra and Number TheorySylow theoremsGrups Teoria deSylow subgroupFitting subgroupCombinatoricsSubgroupLocally finite groupPermutabilityÀlgebraIndex of a subgroupFinite groupMATEMATICA APLICADAMathematicsJournal of Algebra
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On self-normalising subgroups of finite groups

2010

[EN] The aim of this paper is to characterise the classes of groups in which every subnormal subgroup is normal, permutable, or S-permutable by the embedding of the subgroups (respectively, subgroups of prime power order) in their normal, permutable, or S-permutable closure, respectively.

Discrete mathematicsFinite groupPst-groupAlgebra and Number TheoryMathematics::CombinatoricsGrups Teoria deAlgebraMathematics::Group TheoryT-groupPt-groupT-groupPermutabilitySylow permutabilityÀlgebraAlgebra over a fieldFinite groupPermutable closureSubnormal closureMATEMATICA APLICADAGroup theoryMathematics
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