## Torsion units in integral group rings of Janko simple groups.(English)Zbl 1209.16026

Summary: Using the Luthar-Passi method, we investigate the classical Zassenhaus conjecture for the normalized unit group of integral group rings of Janko sporadic simple groups. As a consequence, we obtain that the Gruenberg-Kegel graph of the Janko groups $$J_1$$, $$J_2$$ and $$J_3$$ is the same as that of the normalized unit group of their respective integral group ring.

### MSC:

 16U60 Units, groups of units (associative rings and algebras) 20C05 Group rings of finite groups and their modules (group-theoretic aspects) 16S34 Group rings 20D08 Simple groups: sporadic groups

### Software:

GAP; MINION; LAGUNA
Full Text:

### References:

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