The modular representation algebra of groups with Sylow 2-subgroup Z2 × Z2

Abstract

Let k be a field of characteristic 2 and let G be a finite group. Let A(G) be the modular representation algebra1 over the complex numbers C, formed from kG-modules2. If the Sylow 2-subgroup of G is isomorphic to Z2×Z2, we show that A(G) is semisimple. We make use of the theorems proved by Green [4] and the results of the author concerning A(4) [2], where 4 is the alternating group on 4 symbols.