Search results for "Perfect group"

showing 2 items of 2 documents

Symmetric units and group identities

1998

In this paper we study rings R with an involution whose symmetric units satisfy a group identity. An important example is given by FG, the group algebra of a group G over a field F; in fact FG has a natural involution induced by setting g?g −1 for all group elements g∈G. In case of group algebras if F is infinite, charF≠ 2 and G is a torsion group we give a characterization by proving the following: the symmetric units satisfy a group identity if and only if either the group of units satisfies a group identity (and a characterization is known in this case) or char F=p >0 and 1) FG satisfies a polynomial identity, 2) the p-elements of G form a (normal) subgroup P of G and G/P is a Hamiltonia…

Discrete mathematicsCombinatoricsSubgroupG-moduleMetabelian groupGeneral MathematicsQuaternion groupPerfect groupAlternating groupIdentity componentPermutation groupMathematicsmanuscripta mathematica
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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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