İki-devirli Bir Grubun Integral Grup Halkasındaki Burulmalı Birimsel Elemanlar Üzerine

Abstract

Bu makalede temel amaç,  iki-devirli grubunun  integral grup halkasındaki burulmalı birimsel elemanların yapısını, ikinci dereceden bir kompleks indirgenemez güvenilir temsil kullanarak karakterize etmektir. Birinci Zassenhaus konjektürü (ZC1) ile göstereceğiz ki  integral grup halkasındaki aşikar olmayan burulmalı birimsel elemanlar 3, 4 veya 6 mertebeli ve bunların her biri üç serbest parametre cinsinden ifade edilebilir.

Keywords

• Burulmalı birimsel elemanlar,İntegral grup halkaları,İki-devirli grup,Zassenhaus konjektürleri

On Torsion Units in Integral Group Ring of A Dicyclic Group

Abstract

In this paper, the main aim is to characterize the structure of torsion units in integral group ring  of dicyclic group by using a complex faithful irreducible representation of degree 2. We show by the first of Zassenhaus conjectures (ZC1) that non-trivial torsion units in  are of order 3, 4 or 6 and each of them can be expressed in terms of 3 free parameters.

Keywords

• Torsion units,Integral group rings,Dicyclic Group,Zassenhaus Conjectures

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