# 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.

## 33 Citations

### Torsion Units for some Projected Special Linear Groups

- Mathematics
- 2015

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

- Mathematics
- 2016

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 $S_4(4)$

- Mathematics
- 2015

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

- Mathematics
- 2013

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

- Mathematics
- 2018

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

- Mathematics
- 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…

### Torsion units for some almost simple groups

- MathematicsCzechoslovak 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

- MathematicsProceedings of the Edinburgh Mathematical Society
- 2017

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

- Mathematics
- 2015

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

- MathematicsInt. J. Algebra Comput.
- 2017

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…

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