On the involution module of SL₂(2^ƒ)

Abstract

For any group G the involutions I in G form a G-set under conjugation. The corresponding kG-permutation module kI is known as the involution module of G, with k an algebraically closed field of characteristic two. In this paper we discuss the involution module of the special linear group SL 2 ð2 f Þ. We describe the vertices and the Loewy and Socle Series of all its components.