ZASSENHAUS CONJECTURE FOR INTEGRAL GROUP RING OF SIMPLE LINEAR GROUPS
@article{Gildea2013ZASSENHAUSCF, title={ZASSENHAUS CONJECTURE FOR INTEGRAL GROUP RING OF SIMPLE LINEAR GROUPS}, author={Joe Gildea}, journal={Journal of Algebra and Its Applications}, year={2013}, volume={12}, pages={1-13} }
We prove that the Zassenhaus conjecture is true for PSL(2,8) and PSL(2,17). This is a continuation of research initiated by Kimmerle, Hertweck and Hofert.
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References
SHOWING 1-10 OF 32 REFERENCES
Zassenhaus conjecture for A6
- Mathematics
- 2008
For the alternating group A6 of degree 6, Zassenhaus’ conjecture about rational conjugacy of torsion units in integral group rings is confirmed.
Integral group ring of Rudvalis simple group
- Mathematics
- 2007
Using the Luthar–Passi method, we investigate the classical Zassenhaus conjecture for the normalized unit group of the integral group ring of the Rudvalis sporadic simple group Ru . As a consequence,…
Integral group ring of the Mathieu simple groupM12
- Mathematics
- 2006
We consider the Zassenhaus conjecture for the normalized unit group of the integral group ring of the Mathieu sporadic groupM12. As a consequence, we confirm for this group the Kimmerle’s conjecture…
Integral group ring of the first Mathieu simple group
- Mathematics
- 2006
. We investigated the classical Zassenhaus conjecture for the normalized unit group of the integral group ring of the simple Mathieu group M 11 . As a conse-quence, for this group we confirm the…
INTEGRAL GROUP RING OF THE MCLAUGHLIN SIMPLE GROUP
- Mathematics
- 2007
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…
Integral group ring of the first Mathieu simple group
- Mathematics
- 2007
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…
Integral group ring of the Suzuki sporadic simple group
- MathematicsPublicationes Mathematicae Debrecen
- 2008
Using the Luthar-Passi method, we investigate the classical
Zassenhaus conjecture for the normalized unit group of the
integral group ring of the Suzuki sporadic simple group Suz. As a …
Zassenhaus conjecture forA5
- Mathematics
- 1989
We develop a criterion for rational conjugacy of torsion units of the integral group ringℤG of a finite groupG, as also a necessary condition for an element ofℤG to be a torsion unit, and apply them…
Zassenhaus conjecture for central extensions of S 5
- Mathematics
- 2006
Abstract We confirm a conjecture of Zassenhaus about rational conjugacy of torsion units in integral group rings for a covering group of the symmetric group S 5 and for the general linear group GL(2,…
Torsion units in integral group ring of the Mathieu simple group M22
- Mathematics
- 2007
We investigate the possible character values of torsion units of the normalized unit group of the integral group ring of the Mathieu sporadic group M 22 . We confirm the Kimmerle conjecture on prime…