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Omer Kusmus,
On Torsion Units in Integral Group Ring of A Type of Cyclic-by-Abelian Groups.
Int. J. Math. Comput. Sci., 20, no. 3, (2025), 923-935

DOI:

https://doi.org/10.69793/ijmcs/03.2025/omer

Keywords and phrases:

Group ring, integral group ring, representation, torsion unit, Zassenhaus conjecture.

Abstract:

In this paper, using a complex representation of degree 2 of the group U_{12} which is given in \cite{gamesliebeckU12} and belongs to the class of cyclic-by-abelian groups \cite{caicedo}, we investigate some parametric characteristics of normalized torsion units in integral group ring of U_{12} relying on the fact that all cyclic-by-abelian groups satisfy the first of Zassenhaus conjectures \cite{caicedo}.