On Hochschild cohomology ring of the integral group ring of the quaternion group

Hochschild Cohomology of the Integral Group Ring of the Dihedral Group. I: Even Case

A free bimodule resolution is constructed for the integral group ring of the dihedral group of order 4m. This resolution is applied for a description, in terms of generators and defining relations, of the Hochschild cohomology algebra of this group ring. Introduction Let K be a commutative ring with unity, let R be an associative K-algebra that is a finitely generated projective K-module, let Λ...

Integral Group Ring of Rudvalis Simple Group

Using the Luthar–Passi method, we investigate the classical Zassenhaus conjecture for the normalized unit group of the integral group ring of the Rudvalis sporadic simple group Ru. As a consequence, for this group we confirm Kimmerle’s conjecture on prime graphs.

Inner Products, Group, Ring of Quaternion Numbers

The articles [9], [1], [3], [4], [6], [5], [2], [7], and [8] provide the notation and terminology for this paper. We use the following convention: q, r, c, c1, c2, c3 are quaternion numbers and x1, x2, x3, x4, y1, y2, y3, y4 are elements of R. 0H is an element of H. 1H is an element of H. Next we state several propositions: (1) For all real numbers x, y, z, w holds 〈x, y, z, w〉H = x+y · i+ z · ...

The Cohomology of a Coxeter Group with Group Ring Coefficients

Integral Group Ring of the First Janko Simple Group

We investigate the classical Zassenhaus conjecture for the normalized unit group of the integral group ring of the simple Janko group J1. As a consequence, for this group we confirm Kimmerle’s conjecture on prime graphs.