We compute the cohomology of the Morava stabilizer group S2 at the prime 3 by resolving it by a free product Z=3 Z=3 and analyzing the \relation module."

This paper generalizes the notion of local coefficients and fundamental groups of spaces to simplicial coalgebras. We define a Hopf algebra π1(C) from a simplicial coalgebra C as a generalization of a fundamental group, and show that a module overπ1(C) corresponds to a local coefficient of C. As a consequence, the Hoschild cohomology of a Hopf algebraH with a coefficient M coincides with the co...

we consider the class $mathfrak m$ of $bf r$--modules where $bf r$ is an associative ring. let $a$ be a module over a group ring $bf r$$g$, $g$ be a group and let $mathfrak l(g)$ be the set of all proper subgroups of $g$. we suppose that if $h in mathfrak l(g)$ then $a/c_{a}(h)$ belongs to $mathfrak m$. we investigate an $bf r$$g$--module $a$ such that $g not = g'$, $c_{g}(a) = 1$. we stud...

In this paper, we introduce the notion of BiHom-Lie conformal superalgebras. We develop its representation theory and define cohomology group with coefficients in a module. Finally, derivations superalgebras study some their properties.

Let G be a finite group and let k be a field whose characteristic p divides the order of G. Freyd’s generating hypothesis for the stable module category of G is the statement that a map between finite-dimensional kG-modules in the thick subcategory generated by k factors through a projective if the induced map on Tate cohomology is trivial. We show that if G has periodic cohomology then the gen...

The aim of this thesis is to study profinite groups of type FPn. These are groups G which admit a projective resolution P of Ẑ as a ẐJGK-module such that P0, . . . , Pn are finitely generated, so this property can be studied using the tools of profinite group cohomology. In studying profinite groups it is often useful to consider their cohomology groups with profinite coefficients, but pre-exis...

Let G be a finite group and let k be a field of characteristic p. Given a finitely generated indecomposable non-projective kG-module M , we conjecture that if the Tate cohomology Ĥ ∗ (G, M) of G with coefficients in M is finitely generated over the Tate cohomology ring Ĥ ∗ (G, k), then the support variety VG(M) of M is equal to the entire maximal ideal spectrum VG(k). We prove various results w...

We introduce a generalization of formal local cohomology module, which we call a formal local cohomology module with respect to a pair of ideals and study its various properties. We analyze their structure, the upper and lower vanishing and non-vanishing. There are various exact sequences concerning the formal cohomology modules. Among them a MayerVietoris sequence for two ideals with respect t...

For fields F of characteristic not p containing a primitive pth root of unity, we determine the Galois module structure of the group of pth-power classes of K for all cyclic extensions K/F of degree p. The foundation of the study of the maximal p-extensions of fields K containing a primitive pth root of unity is a group of the pth-power classes of the field: by Kummer theory this group describe...

Let p be an odd prime number and let S be a finite set of prime numbers congruent to 1 modulo p. We prove that the group GS(Q)(p) has cohomological dimension 2 if the linking diagram attached to S and p satisfies a certain technical condition, and we show that GS(Q)(p) is a duality group in these cases. Furthermore, we investigate the decomposition behaviour of primes in the extension QS(p)/Q a...