Search results for "Supersolubility"

showing 2 items of 2 documents

On the exponent of mutually permutable products of two abelian groups

2016

In this paper we obtain some bounds for the exponent of a finite group, and its derived subgroup, which is a mutually permutable product of two abelian subgroups. They improve the ones known for products of finite abelian groups, and they are used to derive some interesting structural properties of such products.

Pure mathematics01 natural sciences0103 physical sciencesNatural sciencemedia_common.cataloged_instancePermutable primeFinite group0101 mathematicsAbelian groupEuropean unionMathematicsmedia_commonFinite groupAlgebra and Number TheoryAbelian groupExponentFactorisations010102 general mathematicsFoundation (engineering)p-LegthAlgebraExponent010307 mathematical physicsMATEMATICA APLICADAp-SupersolubilityJournal of Algebra
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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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