Abstract
Let e : 1→N→G→K→1 be an extension of a finite cyclic group N by a finite cyclic group K, and let R be a commutative ring with 1. Using homological perturbation theory, we construct a free resolution of R over the group ring RG of G in such a way that the resolution reflects the structure of G as an extension of N by K, and we use this resolution to compute the mod p cohomology ring of G for a prime p via the spectral sequence of the extension e.
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