Abstract
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 J1, J2 and J3 is the same as that of the normalized unit group of their respective integral group ring.
Original language | English |
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Pages (from-to) | 593-615 |
Number of pages | 23 |
Journal | Mathematics of Computation |
Volume | 80 |
Issue number | 273 |
DOIs | |
Publication status | Published - 2010 |
Externally published | Yes |
Keywords
- Integral group ring
- Partial augmentation
- Prime graph
- Torsion unit
- Zassenhaus conjecture
ASJC Scopus subject areas
- Algebra and Number Theory
- Computational Mathematics
- Applied Mathematics