TY - JOUR TI - On Torsion Units in Integral Group Ring of A Dicyclic Group AB - Let 𝐺 become an any group. We recall that any two elements of integral group ring ℀𝐺 are rational conjugateprovided that they are conjugate in terms of units in β„šπΊ. Zassenhaus introduced as a conjecture that any unit offinite order in ℀𝐺 is rational conjugate to an element of the group 𝐺. This is known as the first conjecture ofZassenhaus [4]. We denote this conjecture by ZC1 throughout the article. ZC1 has been satisfied for some typesof solvable groups and metacyclic groups. Besides one can see that there exist some counterexamples in metabeliangroups. In this paper, the main aim is to characterize the structure of torsion units in integral group ring ℀𝑇3 ofdicyclic group 𝑇3 = βŸ¨π‘Ž, 𝑏: π‘Ž6 = 1, π‘Ž3 = 𝑏2, π‘π‘Žπ‘βˆ’1 = π‘Žβˆ’1⟩ via utilizing a complex 2nd degree faithful andirreducible representation of ℀𝑇3 which is lifted from a representation of the group 𝑇3. We show by ZC1 that nontrivial torsion units in ℀𝑇3 are of order 3, 4 or 6 and each of them can be stated by 3 free parameters. AU - kusmus, omer PY - 2020 JO - Bitlis Eren Üniversitesi Fen Bilimleri Dergisi VL - 9 IS - 2 SN - 2147-3129 SP - 609 EP - 614 DB - TRDizin UR - http://search/yayin/detay/377925 ER -