Akademik Veri Yönetim Sistemi
Miskolc Mathematical Notes, cilt.25, sa.2, ss.829-838, 2024 (SCI-Expanded)
Presenting an explicit descryption of unit group in the integral group ring of a given non-abelian group is a classical and open problem. Let S3 be a symmetric group of order 6 and C3 be a cyclic group of order 3. In this study, we firstly explore the commensurability in unit group of integral group ring Z(S3×C3) by showing the existence of a subgroup as $$ where Fρ denotes a free group of rank ρ. Later, we introduce an explicit structure of the unit group in Z(S3 ×C3) in terms of semi-direct product of torsion-free normal complement of S3 and the group of units in RS3 where R = Z[ω] is the complex integral domain since ω is the primitive 3rd root of unity. At the end, we give a general method that determines the structure of the unit group of Z(G×C3) for an arbitrary group G depends on torsion-free normal complement V(G) of G in U(Z(G×C3)) in an implicit form. As a consequence, a conjecture which is found in [21] is solved.