The integral cohomology rings of groups of order 𝑝³

Abstract

GENE LEWISC) 0. Introduction. Most of the papers in cohomology of groups have been theoretical The following list describes all the (published and unpublished) computations I am aware of. Atiyah [1, p. 60] calculated the integral (cohomology) ring of the quaternion group Q of order 8. Wall [16] obtained the additive structure of split cyclic-by-cyclic extension. He could not get the ring structure. Cartan-Eilenberg [3, Chapter XII, 7] calculated the cohomology of a cyclic group with any coefficients, and gave an explicit diagonal map. Evens [6] wrote down the cohomology ring of the dihedral group D of order 8. Unfortunately, he did not publish the details of his calculations. Nakaoka [9] calculated the homology ring of symmetric groups with coefficients Zp and in [10, p. 52] found the cohomology ring of S4, coefficients Z2. Cardenas [2] calculated the ring of 2p2, coefficients Zp. Tte