Groups acting on tensor products

Groups Acting on Tensor Products

Groups preserving a distributive product are encountered often in algebra. Examples include automorphism groups of associative and nonassociative rings, classical groups, and automorphism groups of p-groups. While the great variety of such products precludes any realistic hope of describing the general structure of the groups that preserve them, it is reasonable to expect that insight may be ga...

Recognising Tensor Products of Matrix Groups

As a contribution to the project for recognising matrix groups deened over nite elds, we describe an algorithm for deciding whether or not the natural module for such a matrix group can be decomposed into a non-trivial tensor product. In the aarmative case, a tensor decomposition is returned. As one component, we develop algorithms to compute p-local subgroups of a matrix group.

Irreducible Tensor Products over Alternating Groups

On the Tensor Products of Modules for Dihedral 2-Groups

The only groups for which all indecomposable modules are ‘knowable’ are those with cyclic, dihedral, semidihedral, and quaternion Sylow p-subgroups. The structure of the Green ring for groups with cyclic and V4 Sylow p-subgroups are known, but no others have been determined. Of the remaining groups, the dihedral 2-groups have the simplest module category but yet the tensor products of any two i...

On Tensor Products of Modular Representations of Symmetric Groups