On Loewy series of group algebras of some solvable groups (Q910491)

Let p be a prime, let F be a finite field of \(p^{rp}\) elements and let S be the subgroup of the multiplicative group \(F^*\) of F of order \((p^{rp}-1)/(p^ r-1)\). Let G be the (soluble) group generated by the permutation groups U, V, W defined by \(U=\{u_{\beta}:\) \(x\to x+\beta\), \(\beta\in F\}\), \(V=\{v_{\beta}:\) \(x\to \beta x\), \(\beta\in S\}\) and \(W=\{w:\) \(x\to x^{p^ r}\}\). The author obtains, by intricate calculations, the Loewy series of the projective indecomposable modules of G.