The Dade group of (almost) extraspecial \(p\)-groups. (Q1878414)

Let \(k\) be a field of characteristic \(p>0\), and let \(P\) be an (almost) extraspecial \(p\)-group. (An almost extraspecial \(p\)-group is a central product of an extraspecial \(p\)-group with a cyclic group of order \(p^2\).) The authors determine explicit generators and relations for the Dade group \(D_k(P)\); the elements of \(D_k(P)\) are isomorphism classes of indecomposable endo-permutation \(kP\)-modules with vertex \(P\). Their methods make use of the Tits building associated to \(P\).