Related papers: Exponents and the cohomology of finite groups
Computations in the cohomology of finite groups.
PhD thesis concerning cohomological finiteness conditions of infinite discrete groups. Much of the material in this thesis has also appeared in arXiv:1311.7629, arXiv:1310.6262, arXiv:1311.6156, and arXiv:1207.1597.
We give a lower bound for the exponent of certain elements in the integral cohomology of the total spaces of principal BC-bundles for C a finite cyclic group. As applications we give a proof of the theorem of A. Adem and H.-W. Henn that a…
We give an algebraic proof for a theorem of Mislin in the case of cohomology of saturated fusion systems defined on p-groups when p is odd. Some applications of this theorem to block algebras of finite groups are also given.
In this paper, using some properties of fundamental groups and covering spaces of connected polyhedra and CW-complexes, we present topological proof for some famous theorems about finitely presented groups.
In this short paper, we give a $p$-adic analogue of the Hard Leftschetz Theorem.
We prove a cohomological property for a class of finite $p$-groups introduced earlier by M. Y. Xu, which we call semi-abelian $p$-groups. This result implies that a semi-abelian $p$-group has non-inner automorphisms of order $p$, which…
A conjecture of Berkovich asserts that every non-simple finite p-group has a non-inner automorphism of order p. This conjecture is far from being proved despite the great effort devoted to it. In this paper we prove it for p-groups of…
This article is a survey on the cohomology of a reductive algebraic group with coefficients in twisted representations. A large part of the paper is devoted to the advances obtained by the theory of strict polynomial functors initiated by…
Any non-abelian finite $p$-group has a non-inner automorphism of order $p$.
We generalise to profinite groups some of our previous results on the cohomology of pro-p groups of bounded sectional p-rank.
The Hochschild homology and cohomology group can be described in terms of the homology and cohomology of the classifying space of the groupoid of the adjoint action of the group under the suitable assumption of the finiteness of the…
For each odd prime p, we exhibit p-groups G of p-rank two such that (suitably defined) Chern classes of unitary representations of G fail to generate the following rings: 1. The even degree integral cohomology of G; 2. The final page of the…
It is a longstanding conjecture that for a finite group $G$, the exponent of the second homology group $H_2(G, \mathbb{Z})$ divides the exponent of $G$. In this paper, we prove this conjecture for $p$-groups of class at most $p$, finite…
We prove that for any prime $p$ the finite $p$-groups of fixed coclass have only finitely many different mod-$p$ cohomology rings between them. This was conjectured by Carlson; we prove it by first proving a stronger version for groups of…
We exhibit a finitely presented group whose second cohomology contains a weakly bounded, but not bounded, class. As an application, we disprove a long-standing conjecture of Gromov about bounded primitives of differential forms on universal…
We prove the Burghelea Conjecture for groups satisfying some additional cohomological property.
Is the cohomology of the classifying space of a p-compact group, with Noetherian twisted coefficients, a Noetherian module? This note provides, over the ring of p-adic integers, such a generalization to p-compact groups of the Evens-Venkov…
We prove that odd unbounded p-summable Fredholm modules are also bounded p-summable Fredholm modules (this is the odd counterpart of a result of A. Connes for the case of even Fredholm modules).
We determine the mod-p cohomology rings of an infinite family of p-groups, for odd primes p, with cyclic derived subgroups. Our method involves embedding the groups in a compact Lie group of dimension one, and was suggested by P. H.…