We give an affirmative answer to a 1976 question of M. Rosen: every abelian group is isomorphic to the class group of an elliptic Dedekind domain R. We can choose R to be the integral closure of a PID in a separable quadratic field extension. In particular, this yields new and – we feel – simpler proofs of theorems of L. Claborn and C.R. Leedham-Green. Luther Claborn received his PhD from U. Mi...

Let G be an exceptional Lie group with a maximal torus T ⊂ G. We present the integral cohomology ring H∗(G/T ) by a minimal set of Schubert classes on G/T . This completes the program of determining the integral cohomology of all complete flag manifolds G/T in the context of Schubert calculus. The results have been applied in [DZ3] to construct the integral cohomology of a simple Lie group G in...

Let G be an exceptional Lie group with a maximal torus T ⊂ G. We express the integral cohomology ring H(G/T ) by a minimal set of Schubert classes on G/T . This completes the program of determining the integral cohomology of all complete flag manifolds G/T in the context of Schubert calculus. The results are used in [DZ3] to construct the integral cohomology of a simple Lie group G in terms of ...

Let G be an exceptional Lie group with T ⊂ G a maximal torus. We express the integral cohomology ring H(G/T ) by a minimal set of Schubert classes on G/T . This completes the program of determining the integral cohomology of all complete flag manifolds G/T in the context of Schubert calculus. The results are used in [DZ3] to construct the integral cohomology of a simple Lie group G in terms of ...

We investigate the classical Zassenhaus conjecture for the unit group of the integral group ring of Mathieu simple group M 23 using the Luthar-Passi method. This work is a continuation of the research that we carried out for Mathieu groups M 11 and M 12. As a consequence, for this group we confirm Kimmerle's conjecture on prime graphs.

A gauge group is the topological of automorphisms a principal bundle. We compute integral cohomology ring classifying spaces groups U(n)-bundles over 2-sphere by generalizing operation for free loop spaces, called double suspension.