Search results for "Non-abelian group"
showing 8 items of 8 documents
Two groups with isomorphic group algebras
1990
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.
On Finite Solvable Groups That Behave Like Nilpotent Groups with Respect to the Frattini Group
1994
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.
Invariant ordering of surface groups and 3-manifolds which fibre over $S^1$
2006
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.
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.
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.