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

Yıl 2020, , 609 - 614, 15.06.2020

Ömer Küsmüş

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

Öz

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.

Anahtar Kelimeler

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

On Torsion Units in Integral Group Ring of A Dicyclic Group

Öz

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.

Anahtar Kelimeler

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

Kaynakça

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