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Cohomology of metacyclic groups

1991
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Transactions of the American Mathematical Society
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Let e: 1 -> N -► G -► K -> 1 be an extension of a finite cyclic group N by a finite cyclic group K . Using homological perturbation theory, we introduce the beginning of a free resolution of the integers Z over the group ring ZG 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 additive structure of the integral cohomology of G in many cases. We proceed by first establishing a number of special cases,

doi:10.1090/s0002-9947-1991-1031239-1
fatcat:sl3wcfjk2zatje76oz34yokoqe