Loewy Structure for Modules over Semilinear Groups Original Research Article

Let k = image2 be an algebraic closure, G be a finite group, and n be an odd, positive integer. The so-called Cartan integers are the multiplicities of the irreducible kG-modules within the corresponding projective, indecomposable kG-modules. In this paper, formulae for the Cartan integers for the semilinear groups ΣL(2, 2n) are exhibited as quotients of sums of algebraic integers. Additionally, the second Loewy layer of the projective, indecomposable modules are determined. These results extend some results of J. L. Alperin in which he computed the Cartan integers and the second Loewy layer of SL(2, 2n).