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

Year 2020, , 609 - 614, 15.06.2020

Ömer Küsmüş

https://doi.org/10.17798/bitlisfen.624068

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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