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- V. A. Bovdi, Eric Jespers, Alexander Konovalov
- Math. Comput.
- 2011

Using the Luthar-Passi method, we investigate the classical Zassen-haus conjecture for the normalized unit group of integral group rings of Janko simple groups. As a consequence, for the Janko groups J 1 , J 2 and J 3 we confirm Kimmerle's conjecture on prime graphs.

Let V (ZG) be the normalized unit group of the integral group ring ZG of a finite group G. The following famous conjecture was formulated in [10] by H. Zassenhaus: (ZC) Every torsion unit u ∈ V (ZG) is conjugate within the rational group algebra QG to an element of G. This conjecture is already confirmed for several classes of groups but, in general, the… (More)

We consider the Zassenhaus conjecture for the normalized unit group of the integral group ring of the Mathieu sporadic group M 12. As a consequence, we confirm for this group the Kimmerle's conjecture on prime graphs.

- V A Bovdi, A B Konovalov
- 2006

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.

- V A Bovdi, A B Konovalov, S Linton
- 2008

We investigate the possible character values of torsion units of the normalized unit group of the integral group ring of Mathieu sporadic group M 22. We confirm the Kimmerle conjecture on prime graphs for this group and specify the partial augmentations for possible counterexamples to the stronger Zassenhaus conjecture.

- V A Bovdi, A B Konovalov
- 2008

Using the Luthar–Passi method, we investigate the classical Zassen-haus 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.

- V A Bovdi, A B Konovalov
- 2008

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.

- V A Bovdi, A B Konovalov
- 2008

Using the Luthar–Passi method, we investigate the classical Zassen-haus conjecture for the normalized unit group of the integral group ring of the Higman-Sims simple sporadic group HS. As a consequence, we confirm the Kimmerle's conjecture on prime graphs for this sporadic group.

- V A Bovdi, A B Konovalov, E N Marcos
- 2008

Using the Luthar–Passi method, we investigate the classical Zassen-haus conjecture for the normalized unit group of the integral group ring of the Suzuki sporadic simple group Suz. As a consequence, for this group we confirm the Kimmerle's conjecture on prime graphs.

- V A Bovdi, E Jespers, A B Konovalov
- 2006

We investigate the classical Zassenhaus conjecture for the normalized unit group of the integral group ring of the simple Janko group J 1. As a consequence, for this group we confirm Kimmerle's conjecture on prime graphs.