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 consequence, for this group we confirm the Kimmerle’s conjecture on prime graphs.

We investigate the possible character values of torsion units of the normalized unit group of the integral group ring of Mathieu sporadic groupM22. We confirm the Kimmerle conjecture on prime graphs for this group andspecify the partial augmentations for possible counterexamples to the stronger Zassenhaus conjecture.

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, for this group we confirm Kimmerle’s conjecture on prime graphs.

A metabelian group G of order 1440 is constructed which provides a counterexample to a conjecture of Zassenhaus on automorphisms of integral group rings. The group is constructed in the spirit of [8]. An augmented automorphism of ZG which has no Zassenhaus factorization is given explicitly (this was already done in [7] for a group of order 6720), but this time only a few distinguished group rin...

We give a Schinzel-Zassenhaus-type lower bound for the maximum modulus of roots monic integer polynomial with all symmetric respect to unit circle. Our results extend recent work Dimitrov, who proved general Schinzel-Zassenhaus conjecture by using Pólya rationality theorem power series coefficients, and some estimates logarithmic capacity (transfinite diameter) sets. use an enhancement Pólya's ...

In this article, we review the proofs of first Zassenhaus Conjecture on conjugacy torsion units in integral group rings for alternating groups degree 5 and 6, by Luthar-Passi Hertweck. We describe how study these examples led to development two methods – HeLP method lattice method. exhibit summarize some results which were achieved using them. then apply conjecture 7 where only one critical cas...