Araştırma Makalesi
BibTex RIS Kaynak Göster

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

Yıl 2020, , 609 - 614, 15.06.2020
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.

Kaynakça

  • Bächle A. Herman A. Konovalov A. Margolis L. Singh G. 2018. The Status of the Zassenhaus Conjecture for Small Groups, Experimental Mathematics, 27: 431-436.
  • Herman A. Singh G. 2015.Revisiting the Zassenhaus Conjecture on Torsion Units for the Integral Group Rings of Small Groups, Proc. Math. Sci., 125(2): 167-172. Bhandari A. K. Luthar I. S. 1993. Torsion Units of Integral Group Rings of Metacyclic Groups, J. Number Theory, 17: 170-183.
  • Milies C. P. Ritter J. Sehgal S. K. 1986. On A Conjecture of Zassenhaus on Torsion Units in Integral Group Rings II, Proc. Amer. Math. Soc. 97: 201-206.
  • Games D. G. Liebeck M. W. 1986. Representation and Characters of Groups, Cambridge University Press.
  • Hughes I. Pearson K. R. 1972. The Group of Units of the Integral Group Ring ZS_3, Canad. Math. Bull. 15: 529-534.
  • Gildea J. 2013. Zassenhaus Conjecture for Integral Group Rings of Simple Linear Groups, J. Algebra Appl. 12(6).
  • Ari K. 2003. On Torsion Units in the Group Ring ZA_4 and the First Conjecture of Zassenhaus, Int. Math. J. 9(3): 953-958.
  • Caecido M. Margolis L. del Rio A. 2013 Zassenhaus Conjecture for Cyclic-by-Abelian Groups, J. London Math. Soc. 88: 65-78.
  • Hertweck M, 2002. Another Counterexample to a Conjecture of Zassenhaus, Contributions to Algebra and Geometry, 43: 513-520.
  • Hertweck M. 2008. Zassenhaus Conjecture for A_6, Proc. Indian Acad. Sci. (Math. Sci.), 118: 189-195.
  • Hertweck M. 2008. On Torsion Units in Integral Group Rings of Certain Metabelian Groups, Proc. Edinb. Math. Soc. 51: 363-385.
  • Allen P. J. Hobby C. 1987. A Note on The Unit Group of ZS_3, Proc. Amer. Math. Soc. 99: 9-14.
  • Jespers E, Parmenter M. M. 1992. Bicyclic Units in ZS_3, Bull. Belg. Math. Soc., 44: 141-146.
  • Eisele F. Margolis L. 2018. A Counterexample to the first Zassanhaus Conjecture, Advances in Mathematics, 339: 599-641.
  • Sehgal S. K. 1993. Units in Integral Group Rings, Marcel Dekker, New York, Basel.
  • Bilgin T. 2004. Parametrization of Torsion Units in U1(ZS_3), Math. Comput. Appl., 9: 73-77.
  • Bilgin T. 2004. Parametrization of Torsion Units in U1(ZD_4), Int. J. Math. Game Theory Algebra, 14: 83-87.
  • Bilgin T. Ari K. 2007. Parametrization of Torsion Units in U1(ZD_5), Int. J. Algebra, 1: 347-352.

On Torsion Units in Integral Group Ring of A Dicyclic Group

Yıl 2020, , 609 - 614, 15.06.2020
https://doi.org/10.17798/bitlisfen.624068

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.

Kaynakça

  • Bächle A. Herman A. Konovalov A. Margolis L. Singh G. 2018. The Status of the Zassenhaus Conjecture for Small Groups, Experimental Mathematics, 27: 431-436.
  • Herman A. Singh G. 2015.Revisiting the Zassenhaus Conjecture on Torsion Units for the Integral Group Rings of Small Groups, Proc. Math. Sci., 125(2): 167-172. Bhandari A. K. Luthar I. S. 1993. Torsion Units of Integral Group Rings of Metacyclic Groups, J. Number Theory, 17: 170-183.
  • Milies C. P. Ritter J. Sehgal S. K. 1986. On A Conjecture of Zassenhaus on Torsion Units in Integral Group Rings II, Proc. Amer. Math. Soc. 97: 201-206.
  • Games D. G. Liebeck M. W. 1986. Representation and Characters of Groups, Cambridge University Press.
  • Hughes I. Pearson K. R. 1972. The Group of Units of the Integral Group Ring ZS_3, Canad. Math. Bull. 15: 529-534.
  • Gildea J. 2013. Zassenhaus Conjecture for Integral Group Rings of Simple Linear Groups, J. Algebra Appl. 12(6).
  • Ari K. 2003. On Torsion Units in the Group Ring ZA_4 and the First Conjecture of Zassenhaus, Int. Math. J. 9(3): 953-958.
  • Caecido M. Margolis L. del Rio A. 2013 Zassenhaus Conjecture for Cyclic-by-Abelian Groups, J. London Math. Soc. 88: 65-78.
  • Hertweck M, 2002. Another Counterexample to a Conjecture of Zassenhaus, Contributions to Algebra and Geometry, 43: 513-520.
  • Hertweck M. 2008. Zassenhaus Conjecture for A_6, Proc. Indian Acad. Sci. (Math. Sci.), 118: 189-195.
  • Hertweck M. 2008. On Torsion Units in Integral Group Rings of Certain Metabelian Groups, Proc. Edinb. Math. Soc. 51: 363-385.
  • Allen P. J. Hobby C. 1987. A Note on The Unit Group of ZS_3, Proc. Amer. Math. Soc. 99: 9-14.
  • Jespers E, Parmenter M. M. 1992. Bicyclic Units in ZS_3, Bull. Belg. Math. Soc., 44: 141-146.
  • Eisele F. Margolis L. 2018. A Counterexample to the first Zassanhaus Conjecture, Advances in Mathematics, 339: 599-641.
  • Sehgal S. K. 1993. Units in Integral Group Rings, Marcel Dekker, New York, Basel.
  • Bilgin T. 2004. Parametrization of Torsion Units in U1(ZS_3), Math. Comput. Appl., 9: 73-77.
  • Bilgin T. 2004. Parametrization of Torsion Units in U1(ZD_4), Int. J. Math. Game Theory Algebra, 14: 83-87.
  • Bilgin T. Ari K. 2007. Parametrization of Torsion Units in U1(ZD_5), Int. J. Algebra, 1: 347-352.
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Ömer Küsmüş 0000-0001-7397-0735

Yayımlanma Tarihi 15 Haziran 2020
Gönderilme Tarihi 24 Eylül 2019
Kabul Tarihi 8 Nisan 2020
Yayımlandığı Sayı Yıl 2020

Kaynak Göster

IEEE Ö. Küsmüş, “On Torsion Units in Integral Group Ring of A Dicyclic Group”, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, c. 9, sy. 2, ss. 609–614, 2020, doi: 10.17798/bitlisfen.624068.



Bitlis Eren Üniversitesi
Fen Bilimleri Dergisi Editörlüğü

Bitlis Eren Üniversitesi Lisansüstü Eğitim Enstitüsü        
Beş Minare Mah. Ahmet Eren Bulvarı, Merkez Kampüs, 13000 BİTLİS        
E-posta: fbe@beu.edu.tr