Periodic modules of large periods for extra-special \(p\)-groups (Q1173861)

For an odd prime \(p\) and a field \(k\) of characteristic \(p\), the author constructs certain \(kG\)-modules for \(G\) the extra special \(p\)-group of order \(p^ 3\) and exponent \(p\). These modules arise as kernels of cocycles representing particular homogeneous elements of the cohomology algebra of \(G\) (with coefficients in \(k\)). For special choices one obtains in this way indecomposable periodic \(kG\)-modules of period \(2p\). These are used to study the structure of the cohomology algebra of \(G\) but a result is only obtained modulo elements of degree less than \(2p+1\).