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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)

- 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.

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, 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, 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, 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
- 2008

We consider the Zassenhaus conjecture for the normalized unit group of the integral group ring of the Mathieu sporadic group M 24. As a consequence, for this group we confirm Kimmerle's conjecture on prime graphs.