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.

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 ‎previous results we confirm the prime graph‎ ‎conjecture for integral group rings of $a_n$ for all $n leq 10$‎.

For the alternating group A6 of degree 6, Zassenhaus’ conjecture about rational conjugacy of torsion units in integral group rings is confirmed.

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 conjecture on prime graphs.

Using the Luthar–Passi method, we investigate the Zassenhaus and Kimmerle conjectures for normalized unit groups of integral group rings of the Held and O’Nan sporadic simple groups. We confirm the Kimmerle conjecture for the Held simple group and also derive for both groups some extra information relevant to the classical Zassenhaus conjecture. Let U(ZG) be the unit group of the integral group...

We consider the Zassenhaus conjecture for the normalized unit group of the integral group ring of the Mathieu sporadic group M 12. As a consequence, we confirm for this group the Kimmerle's conjecture on prime graphs.

We investigate the classical Zassenhaus conjecture for the normalized unit group of the integral group ring of the simple Janko group J1. As a consequence, for this group we confirm Kimmerle’s conjecture on prime graphs.

We investigate the Zassenhaus Conjecture for the integral group ring of the simple group PSL(3, 4).

Using the Luthar-Passi method, we investigate the classical Zassenhaus conjecture for the normalized unit group of integral group rings of Janko simple groups. As a consequence, for the Janko groups J1, J2 and J3 we confirm Kimmerle’s conjecture on prime graphs.