A Remark on Relative Homology and Cohomology Groups of a Group

a remark on group rings of periodic groups

a positive solution of the problem of the existence of nontrivial pairs of zero-divisors in group rings of free burnside groups of sufficiently large odd periods $n>10^{10}$ obtained previously by s. v. ivanov and r. mikhailov extended to all odd periods $ngeq 665$‎.

A primer on computational group homology and cohomology

Continuous cohomology and homology of profinite groups

Let G be a profinite group with a countable basis of neighborhoods of the identity. A cohomology and homology theory for the group G with non-discrete topological coefficients is developed, improving previous expositions of the subject (see [Wi], [R–Z] and [S-W]). Though the category of topological G-modules considered is additive but not abelian, there is a theory of derived functors. All stan...

The Homology and Cohomology Groups of H3

A free resolution of Z for the integral group ring of the three-dimensional Heisenberg group has been constructed by extending Lyndon’s partial resolution. The integral homology and cohomology have been calculated from there. 3 H AMS Classification: 18G, 20J.

On Exponents of Homology and Cohomology of Finite Groups

Let G be a finite group and let r be the maximum of the p-ranks of G for all primes p dividing the order to G. There exist positive integers m and n such that the exponents of Hn(G,Z) and Hm(G, Z) are greater than Suppose that G is a finite group. It has long been known that the exponent of Hn(G, Z) divides |G|, the order of G, for all n > 0. Beyond this fact very little has been established co...