Wreath Products in the Unit Group of Modular Group Algebras of 2-groups of Maximal Class

We study the unit group of the modular group algebra KG, where G is a 2-group of maximal class. We prove that the unit group of KG possesses a section isomorphic to the wreath product of a group of order two with the commutator subgroup of the group G.Comment: 12 pages, LaTe

Integral group ring of the first Mathieu simple group

We investigate the classical Zassenhaus conjecture for the normalized unit group of the integral group ring of the simple Mathieu group M11. As a consequence, for this group we confirm the conjecture by Kimmerle about prime graphs

Integral group ring of the McLaughlin simple group

We consider the Zassenhaus conjecture for the normalized unit group of the integral group ring of the McLaughlin sporadic group McL. As a consequence, we confirm for this group the Kimmerle’s conjecture on prime graphs

Kimmerle conjecture for the Held and O'Nan sporadic simple groups

Using the Luthar--Passi method, we investigate the Zassenhaus and Kimmerle conjectures for normalized unit groups of integral group rings of the Held and O'Nan sporadic simple groups. We confirm the Kimmerle conjecture for the Held simple group and also derive for both groups some extra information relevant to the classical Zassenhaus conjecture