Search results for "Finite soluble group"

showing 3 items of 3 documents

On finite T-groups

2003

[EN] Characterisations of finite groups in which normality is a transitive relation are presented in the paper. We also characterise the finite groups in which every subgroup is either permutable or coincides with its permutiser as the groups in which every subgroup is permutable.

Mathematics::Group TheoryMathematics::CombinatoricsFinite soluble groupTransitive normalityMATEMATICA APLICADAMatemàtica
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ON A QUESTION OF BEIDLEMAN AND ROBINSON

2002

[EN] In [J. C. Beidleman, D. J. S. Robinson, J. Algebra 1997, 191, 686--703, Theorem A], Beidleman and Robinson proved that if a group satisfies the permutizer condition, it is soluble, its chief factors have order a prime number or 4 and G induces the full group of automorphisms in the chief factors of order 4. In this paper, we show that the converse of this theorem is false by showing some counterexamples. We also find some sufficient conditions for a group satisfying the converse of that theorem to satisfy the permutizer condition.

Pure mathematicsAlgebra and Number TheoryFinite soluble groupGroup (mathematics)Permutizer conditionPrime numberGrups Teoria deAutomorphismCombinatoricsConverseChief factorOrder (group theory)ÀlgebraAlgebra over a fieldMATEMATICA APLICADAMathematicsCounterexampleCommunications in Algebra
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On totally permutable products of finite groups

2005

[EN] The behaviour of totally permutable products of finite groups with respect to certain classes of groups is studied in the paper. The results are applied to obtain information about totally permutable products of T, PT, and PST-groups.

AlgebraTotally permutable productAlgebra and Number TheoryMathematics::CombinatoricsTransitive permutabilityFinite soluble groupFinite nilpotent groupFormationPermutable primeAlgebra over a fieldMATEMATICA APLICADAMatemàticaMathematics
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