Search results for "G-module"
showing 6 items of 6 documents
A presentation and a representation of the Held group
1996
In this note we give a brief description of a new presentation of the Held group, which is deduced only from the original work of D. Held in 1969, who shows that a finite simple group, having the same centralizer of a 2-central involution as in the Mathieu group M24, is M24, L5(2) or a group of order 4.030.387.200. The first complete uniqueness proof for the latter case was given by L. Soicher in 1991. The generators and relations occurring here are easy to verify by a simple Todd–Coxeter algorithm. It is an easy task to get a new uniqueness and existence proof of the Held group from this result. Also basic facts like the Schur Multiplier or the automorphism group of the Held group follow f…
Group algebras whose units satisfy a group identity
1997
Let F G FG be the group algebra of a torsion group over an infinite field F F . Let U U be the group of units of F G FG . We prove that if U U satisfies a group identity, then F G FG satisfies a polynomial identity. This confirms a conjecture of Brian Hartley.
Abelian gradings on upper-triangular matrices
2003
Let G be an arbitrary finite abelian group. We describe all possible G-gradings on an upper-triangular matrix algebra over an algebraically closed field of characteristic zero.
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…
Symmetric (79, 27, 9)-designs Admitting a Faithful Action of a Frobenius Group of Order 39
1997
AbstractIn this paper we present the classification of symmetric designs with parameters (79, 27, 9) on which a non-abelian group of order 39 acts faithfully. In particular, we show that such a group acts semi-standardly with 7 orbits. Using the method of tactical decompositions, we are able to construct exactly 1320 non-isomorphic designs. The orders of the full automorphism groups of these designs all divide 8 · 3 · 13.
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.