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}
}
  • J. Gildea
  • Published 9 May 2013
  • Mathematics
  • Journal of Algebra and Its Applications
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. 

Tables from this paper

Torsion Units for some Projected Special Linear Groups

In this paper, we investigate the Zassenhaus conjecture for $PSL(4,3)$ and $PSL(5,2)$. Consequently, we prove that the Prime graph question is true for both groups.

Torsion units for some untwisted exceptional groups of lie type

In this paper, we investigate the Zassenhaus conjecture for exceptional groups of lie type G2(q) for q = {3, 4}. Consequently, we prove that the Prime graph question is true for these groups.

Torsion units of integral group ring of the simple group $S_4(4)$

We consider the Zassenhaus conjecture for the normalized unit group of the integral group ring of the sympletic simple group S4.4/. As a consequence, we confirm for this group the prime graph

The prime graph conjecture for integral group rings of some alternatings groups

We investigate the classical H. Zassenhaus conjecture‎ ‎for integral group rings of alternating groups $A_9$ and $A_{10}$ of degree‎ ‎$9$ and $10$‎, ‎respectively‎. ‎As a consequence of our‎

Finite Subgroups of Group Rings: A survey

In the 1940's Graham Higman initiated the study of finite subgroups of the unit group of an integral group ring. Since then many fascinating aspects of this structure have been discovered. Major

Torsion units for some almost simple groups

We investigate the Zassenhaus conjecture regarding rational conjugacy of torsion units in integral group rings for certain automorphism groups of simple groups. Recently, many new restrictions on

Torsion units for some almost simple groups

  • J. Gildea
  • Mathematics
    Czechoslovak Mathematical Journal
  • 2016
We investigate the Zassenhaus conjecture regarding rational conjugacy of torsion units in integral group rings for certain automorphism groups of simple groups. Recently, many new restrictions on

Rational Conjugacy of Torsion Units in Integral Group Rings of Non-Solvable Groups

Abstract We introduce a new method to study rational conjugacy of torsion units in integral group rings using integral and modular representation theory. Employing this new method, we verify the

On the torsion units of the integral group ring of finite projective special linear groups

ABSTRACT H. J. Zassenhaus conjectured that any unit of finite-order and augmentation one in the integral group ring of a finite group G is conjugate in the rational group algebra to an element of G.

On the Prime Graph Question for Integral Group Rings of 4-Primary Groups II

In this article the study of the Prime Graph Question for the integral group ring of almost simple groups which have an order divisible by exactly 4 different primes is continued. We provide more

References

SHOWING 1-10 OF 32 REFERENCES

Zassenhaus conjecture for A6

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

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

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

. 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

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

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

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

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

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

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