Search results for "Non-abelian group"

showing 8 items of 8 documents

Two groups with isomorphic group algebras

1990

CombinatoricsClassification of Clifford algebrasGroup isomorphismDicyclic groupGeneral MathematicsSimple groupQuaternion groupCyclic groupCycle graph (algebra)MathematicsNon-abelian groupArchiv der Mathematik
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Group algebras of torsion groups and Lie nilpotence

2010

Letbe an involution of a group algebra FG induced by an involution of the group G. For char F 0 2, we classify the torsion groups G with no elements of order 2 whose Lie al- gebra of � -skew elements is nilpotent.

Discrete mathematicsPure mathematicsAlgebra and Number TheorySimple Lie groupAdjoint representationANÉIS DE GRUPOSGroup algebraRepresentation theoryGraded Lie algebraNon-abelian groupRepresentation of a Lie groupgroup algebra unitNilpotent groupMathematicsJournal of Group Theory
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On Finite Solvable Groups That Behave Like Nilpotent Groups with Respect to the Frattini Group

1994

Discrete mathematicsPure mathematicsAlgebra and Number TheoryGroup (mathematics)Solvable groupExtra special groupSimple groupNilpotent groupCentral seriesFitting subgroupMathematicsNon-abelian groupJournal of Algebra
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Group Identities on Units of Group Algebras

2000

Abstract Let U be the group of units of the group algebra FG of a group G over a field F . Suppose that either F is infinite or G has an element of infinite order. We characterize groups G so that U satisfies a group identity. Under the assumption that G modulo the torsion elements is nilpotent this gives a complete classification of such groups. For torsion groups this problem has already been settled in recent years.

p-groupAlgebra and Number TheoryDicyclic groupG-module010102 general mathematicsPerfect groupCyclic group010103 numerical & computational mathematics01 natural sciencesNon-abelian groupCombinatoricsInfinite groupIdentity component0101 mathematicsMathematicsJournal of Algebra
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Invariant ordering of surface groups and 3-manifolds which fibre over $S^1$

2006

CombinatoricsDicyclic groupGeneral MathematicsInvariant (mathematics)Point groups in two dimensionsCovering groups of the alternating and symmetric groupsMathematicsNon-abelian groupMathematical Proceedings of the Cambridge Philosophical Society
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On a class of generalised Schmidt groups

2015

In this paper families of non-nilpotent subgroups covering the non-nilpotent part of a finite group are considered. An A 5 -free group possessing one of these families is soluble, and soluble groups with this property have Fitting length at most three. A bound on the number of primes dividing the order of the group is also obtained.

Group (mathematics)Applied MathematicsMathematics::Rings and AlgebrasGrups Teoria deCycle graph (algebra)Sporadic groupFinite groupsNon-abelian groupCombinatoricsMathematics::Group TheoryGroup of Lie typeLocally finite groupSimple groupNilpotent groupsMaximal subgroupsOrder (group theory)ÀlgebraMATEMATICA APLICADAMathematics::Representation TheoryMathematicsAnnali di Matematica Pura ed Applicata (1923 -)
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A class of finite groups having nilpotent injectors

1986

AbstractThe purpose of this paper is to construct a class of groups which properly contains the class of N-constrained groups, and which is such that all groups in this class have N-injectors.

Discrete mathematicsPure mathematicsNilpotentClass (set theory)Group of Lie typeGeneral MedicineCA-groupCycle graph (algebra)Nilpotent groupMathematicsNon-abelian groupJournal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
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Transitive permutation groups in which all derangements are involutions

2006

AbstractLet G be a transitive permutation group in which all derangements are involutions. We prove that G is either an elementary abelian 2-group or is a Frobenius group having an elementary abelian 2-group as kernel. We also consider the analogous problem for abstract groups, and we classify groups G with a proper subgroup H such that every element of G not conjugate to an element of H is an involution.

CombinatoricsSubgroupAlgebra and Number TheorySymmetric groupPrimitive permutation groupElementary abelian groupAbelian groupFrobenius groupCyclic permutationMathematicsNon-abelian groupJournal of Pure and Applied Algebra
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