Normalizer property for integral group rings of nite groups

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.

Class-preserving Automorphisms and the Normalizer Property for Blackburn Groups

For a group G, let U be the group of units of the integral group ring ZG. The group G is said to have the normalizer property if NU (G) = Z(U)G. It is shown that Blackburn groups have the normalizer property. These are the groups which have non-normal finite subgroups, with the intersection of all of them being nontrivial. Groups G for which class-preserving automorphisms are inner automorphism...

Central Units of Integral Group Rings of Nilpotent Groups

In this paper a finite set of generators is given for a subgroup of finite index in the group of central units of the integral group ring of a finitely generated nilpotent group. In this paper we construct explicitly a finite set of generators for a subgroup of finite index in the centre Z(U(ZG)) of the unit group U(ZG) of the integral group ring ZG of a finitely generated nilpotent group G. Ri...

On Torsion Subgroups in Integral Group Rings of Finite Groups