Search results for "Factorised group"

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On sigma-subnormal subgroups of factorised finite groups

2020

Abstract Let σ = { σ i : i ∈ I } be a partition of the set P of all prime numbers. A subgroup X of a finite group G is called σ-subnormal in G if there is chain of subgroups X = X 0 ⊆ X 1 ⊆ ⋯ ⊆ X n = G with X i − 1 normal in X i or X i / C o r e X i ( X i − 1 ) is a σ i -group for some i ∈ I , 1 ≤ i ≤ n . In the special case that σ is the partition of P into sets containing exactly one prime each, the σ-subnormality reduces to the familiar case of subnormality. If a finite soluble group G = A B is factorised as the product of the subgroups A and B, and X is a subgroup of G such that X is σ-subnormal in 〈 X , X g 〉 for all g ∈ A ∪ B , we prove that X is σ-subnormal in G. This is an extension…

Finite groupAlgebra and Number TheorySoluble group010102 general mathematicsPrime number01 natural sciencesCombinatorics0103 physical sciencesPartition (number theory)010307 mathematical physics0101 mathematicsFinite groupSigma-Subnormal subgroupSigma-NilpotencyMATEMATICA APLICADAFactorised groupMathematics
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SOME SOLUBILITY CRITERIA IN FACTORISED GROUPS

2012

In this paper, solubility of groups factorised as a product of two subgroups which are connected by certain permutability properties is studied.

Soluble groupComputational chemistryGeneral MathematicsProduct (mathematics)Mutually m-permutable productSolubilityMATEMATICA APLICADAFactorised groupMathematicsBulletin of the Australian Mathematical Society
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