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RESEARCH PRODUCT
Maximal subgroups and PST-groups
V. Pérez-calabuigRamon Esteban-romeroRamon Esteban-romeroJames C. BeidlemanAdolfo Ballester-bolinchessubject
20e2820d05General MathematicsCombinatoricsLocally finite groupPermutabilityQA1-939Permutable prime20d10Algebra over a fieldMathematicsDiscrete mathematicsTransitive relation20f16Group (mathematics)20e15Sylow theoremsGrups Teoria deSylow-permutabilitySupersolubilityFinite groupsNumber theoryMaximal subgroupsÀlgebraMATEMATICA APLICADAMathematicsdescription
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 of Kaplan's results, which enables a better understanding of the relationships between these classes.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2013-06-01 |