Displaying 21 – 40 of 232

Showing per page

Bilinear forms for SL(2,q), An and similar groups.

Alexandre Turull (1992)

Publicacions Matemàtiques

The set of invariant symmetric bilinear forms on irreducible modules over fields of characteristic zero for certain groups is studied. Results are obtained under the presence in a finite group of elements of order four whose square is central. In particular, we find that the relevant modules for the groups mentioned in the title always accept an invariant symmetric bilinear form under which the module admits an orthonormal basis.

Brauer relations in finite groups

Alex Bartel, Tim Dokchitser (2015)

Journal of the European Mathematical Society

If G is a non-cyclic finite group, non-isomorphic G -sets X , Y may give rise to isomorphic permutation representations [ X ] [ Y ] . Equivalently, the map from the Burnside ring to the rational representation ring of G has a kernel. Its elements are called Brauer relations, and the purpose of this paper is to classify them in all finite groups, extending the Tornehave–Bouc classification in the case of p -groups.

Centralizers of gap groups

Toshio Sumi (2014)

Fundamenta Mathematicae

A finite group G is called a gap group if there exists an ℝG-module which has no large isotropy groups except at zero and satisfies the gap condition. The gap condition facilitates the process of equivariant surgery. Many groups are gap groups and also many groups are not. In this paper, we clarify the relation between a gap group and the structures of its centralizers. We show that a nonsolvable group which has a normal, odd prime power index proper subgroup is a gap group.

Characterizing projective general unitary groups PGU 3 ( q 2 ) by their complex group algebras

Farrokh Shirjian, Ali Iranmanesh (2017)

Czechoslovak Mathematical Journal

Let G be a finite group. Let X 1 ( G ) be the first column of the ordinary character table of G . We will show that if X 1 ( G ) = X 1 ( PGU 3 ( q 2 ) ) , then G PGU 3 ( q 2 ) . As a consequence, we show that the projective general unitary groups PGU 3 ( q 2 ) are uniquely determined by the structure of their complex group algebras.

Currently displaying 21 – 40 of 232