A dichotomy for integral group rings via higher modular groups as amalgamated products

Class Groups of Integral Group Rings(x)

Let A be an Ä-order in a semisimple finite dimensional /(-algebra, where K is an algebraic number field, and R is the ring of algebraic integers of K. Denote by C(A) the reduced class group of the category of locally free left A-lattices. Choose A= ZC, the integral group ring of a finite group G, and let A be a maximal Z-order in QG containing A. There is an epimorphism C(A)-C(A'), given by JIÍ...

Kimmerle’s Conjecture for Integral Group Rings of Some Alternating Groups

Using the Luthar–Passi method and results of Hertweck, we study the long-standing conjecture of Zassenhaus for integral group rings of alternating groups An, n ≤ 8. As a consequence of our results, we confirm the Kimmerle’s conjecture about prime graphs for those groups.

Amalgamated Products and Properly 3-realizable Groups

In this paper, we show that the class of all properly 3-realizable groups is closed under amalgamated free products (and HNN-extensions) over finite groups. We recall that G is said to be properly 3-realizable if there exists a compact 2-polyhedron K with π1(K) = G and whose universal cover K̃ has the proper homotopy type of a 3-manifold (with boundary).

On Torsion Subgroups in Integral Group Rings of Finite Groups

Torsion units in integral group rings of Janko simple groups

Using the Luthar-Passi method, we investigate the classical Zassenhaus conjecture for the normalized unit group of integral group rings of Janko simple groups. As a consequence, for the Janko groups J1, J2 and J3 we confirm Kimmerle’s conjecture on prime graphs.