BibTex RIS Kaynak Göster

The unit group of group algebra $F_qSL(2;Z_3)$

Yıl 2016, Cilt: 3 Sayı: 1, 1 - 6, 11.01.2016
https://doi.org/10.13069/jacodesmath.83854

Öz

Let $\F_q$ be a finite field of characteristic $p$ having $q$ elements, where $q = p^k$ and $p\ge 5$.  Let $ SL(2,\Z_3)$ be the special linear group of $2\times2$ matrices with determinant $1$ over $\Z_3$. In this note we establish the structure of the unit group of $\F_q SL(2,\Z_3)$.

Kaynakça

  • L. Creedon, J. Gildea, The structure of the unit group of the group algebra F2kD, Canad. Math. Bull. 54(2) (2011) 237–243.
  • R. A. Ferraz, Simple components of the center of FG/J(FG), Comm. Algebra 36(9) (2008) 3191–3199.
  • J. Gildea, The structure of the unit group of the group algebra FkA4, Czechoslovak Math. J. 61(2) (2011) 531–539.
  • J. Gildea, F. Monaghan, Units of some group algebras of groups of order 12 over any finite field of characteristic 3, Algebra Discrete Math. 11(1) (2011) 46–58
  • P. R. Helm, A presentation for SL(2, Zpr), Comm. Algebra 10(15) (1982) 1683–1688.
  • T. Hurley, Group rings and ring of matrices, Int. J. Pure Appl. Math. 31(3) (2006) 319–335.
  • T. Hurley, Convolutional codes from units in matrix and group rings, Int. J. Pure Appl. Math. 50(3) (2009) 431–463
  • R. Lidl, H. Niederreiter, Introduction to finite fields and their applications, Cambridge University Press, New York, 2000.
  • N. Makhijani, Units in finite group algebras, IIT Delhi, 2014.
  • N. Makhijani, R. K. Sharma, J. B. Srivastava, A note on units in FpmD2pn, Acta Math. Acad. Paedagog. Nyházi. 30(1) (2014) 17–25.
  • N. Makhijani, R. K. Sharma, J. B. Srivastava, The unit group of algebra of circulant matrices, Int. J. Group Theory. 3(4) (2014) 13–16
  • N. Makhijani, R. K. Sharma, J. B. Srivastava, The unit group of Fq[D30], Serdica Math. J. 41(2-3) (2015) 185–198.
  • C. P. Milies, S. K. Sehgal, An introduction to group rings, Kluwer Academic Publishers, 2002.
  • S. Perlis, G. L. Walker, Abelian group algebras of finite order, Trans. Amer. Math. Soc. 68(3) (1950) –426
  • R. K. Sharma, J. B. Srivastava, M. Khan, The unit group of FA4, Publ. Math. Debrecen 71(1-2) (2007) 21–26.
  • R. K. Sharma, J. B. Srivastava, M. Khan, The unit group of FS3, Acta Math. Acad. Paedagog. Nyházi. 23(2) (2007) 129–142.
  • R. K. Sharma, P. Yadav, Unit group of algebra of circulant matrices, Int. J. Group Theory. 2(4) (2013) 1–6
  • R. K. Sharma, P. Yadav, The unit group of ZpQ8, Algebras Groups Geom. 25(4) (2008) 425–429.
  • G. Tang, Y. Wei, Nanning, Y. Li, Units group of group algebras of some small groups, Czechoslovak Math. J. 64(1) (2014) 149–157.
Yıl 2016, Cilt: 3 Sayı: 1, 1 - 6, 11.01.2016
https://doi.org/10.13069/jacodesmath.83854

Öz

Kaynakça

  • L. Creedon, J. Gildea, The structure of the unit group of the group algebra F2kD, Canad. Math. Bull. 54(2) (2011) 237–243.
  • R. A. Ferraz, Simple components of the center of FG/J(FG), Comm. Algebra 36(9) (2008) 3191–3199.
  • J. Gildea, The structure of the unit group of the group algebra FkA4, Czechoslovak Math. J. 61(2) (2011) 531–539.
  • J. Gildea, F. Monaghan, Units of some group algebras of groups of order 12 over any finite field of characteristic 3, Algebra Discrete Math. 11(1) (2011) 46–58
  • P. R. Helm, A presentation for SL(2, Zpr), Comm. Algebra 10(15) (1982) 1683–1688.
  • T. Hurley, Group rings and ring of matrices, Int. J. Pure Appl. Math. 31(3) (2006) 319–335.
  • T. Hurley, Convolutional codes from units in matrix and group rings, Int. J. Pure Appl. Math. 50(3) (2009) 431–463
  • R. Lidl, H. Niederreiter, Introduction to finite fields and their applications, Cambridge University Press, New York, 2000.
  • N. Makhijani, Units in finite group algebras, IIT Delhi, 2014.
  • N. Makhijani, R. K. Sharma, J. B. Srivastava, A note on units in FpmD2pn, Acta Math. Acad. Paedagog. Nyházi. 30(1) (2014) 17–25.
  • N. Makhijani, R. K. Sharma, J. B. Srivastava, The unit group of algebra of circulant matrices, Int. J. Group Theory. 3(4) (2014) 13–16
  • N. Makhijani, R. K. Sharma, J. B. Srivastava, The unit group of Fq[D30], Serdica Math. J. 41(2-3) (2015) 185–198.
  • C. P. Milies, S. K. Sehgal, An introduction to group rings, Kluwer Academic Publishers, 2002.
  • S. Perlis, G. L. Walker, Abelian group algebras of finite order, Trans. Amer. Math. Soc. 68(3) (1950) –426
  • R. K. Sharma, J. B. Srivastava, M. Khan, The unit group of FA4, Publ. Math. Debrecen 71(1-2) (2007) 21–26.
  • R. K. Sharma, J. B. Srivastava, M. Khan, The unit group of FS3, Acta Math. Acad. Paedagog. Nyházi. 23(2) (2007) 129–142.
  • R. K. Sharma, P. Yadav, Unit group of algebra of circulant matrices, Int. J. Group Theory. 2(4) (2013) 1–6
  • R. K. Sharma, P. Yadav, The unit group of ZpQ8, Algebras Groups Geom. 25(4) (2008) 425–429.
  • G. Tang, Y. Wei, Nanning, Y. Li, Units group of group algebras of some small groups, Czechoslovak Math. J. 64(1) (2014) 149–157.
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Makaleler
Yazarlar

Swati Maheshwari Bu kişi benim

R. K. Sharma Bu kişi benim

Yayımlanma Tarihi 11 Ocak 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 3 Sayı: 1

Kaynak Göster

APA Maheshwari, S., & Sharma, R. K. (2016). The unit group of group algebra $F_qSL(2;Z_3)$. Journal of Algebra Combinatorics Discrete Structures and Applications, 3(1), 1-6. https://doi.org/10.13069/jacodesmath.83854
AMA Maheshwari S, Sharma RK. The unit group of group algebra $F_qSL(2;Z_3)$. Journal of Algebra Combinatorics Discrete Structures and Applications. Ocak 2016;3(1):1-6. doi:10.13069/jacodesmath.83854
Chicago Maheshwari, Swati, ve R. K. Sharma. “The Unit Group of Group Algebra $F_qSL(2;Z_3)$”. Journal of Algebra Combinatorics Discrete Structures and Applications 3, sy. 1 (Ocak 2016): 1-6. https://doi.org/10.13069/jacodesmath.83854.
EndNote Maheshwari S, Sharma RK (01 Ocak 2016) The unit group of group algebra $F_qSL(2;Z_3)$. Journal of Algebra Combinatorics Discrete Structures and Applications 3 1 1–6.
IEEE S. Maheshwari ve R. K. Sharma, “The unit group of group algebra $F_qSL(2;Z_3)$”, Journal of Algebra Combinatorics Discrete Structures and Applications, c. 3, sy. 1, ss. 1–6, 2016, doi: 10.13069/jacodesmath.83854.
ISNAD Maheshwari, Swati - Sharma, R. K. “The Unit Group of Group Algebra $F_qSL(2;Z_3)$”. Journal of Algebra Combinatorics Discrete Structures and Applications 3/1 (Ocak 2016), 1-6. https://doi.org/10.13069/jacodesmath.83854.
JAMA Maheshwari S, Sharma RK. The unit group of group algebra $F_qSL(2;Z_3)$. Journal of Algebra Combinatorics Discrete Structures and Applications. 2016;3:1–6.
MLA Maheshwari, Swati ve R. K. Sharma. “The Unit Group of Group Algebra $F_qSL(2;Z_3)$”. Journal of Algebra Combinatorics Discrete Structures and Applications, c. 3, sy. 1, 2016, ss. 1-6, doi:10.13069/jacodesmath.83854.
Vancouver Maheshwari S, Sharma RK. The unit group of group algebra $F_qSL(2;Z_3)$. Journal of Algebra Combinatorics Discrete Structures and Applications. 2016;3(1):1-6.