대한수학회지 (Journal of the Korean Mathematical Society)

  • 제47권6호
  • /
  • Pages.1239-1252
  • /
  • 2010
  • /
  • 0304-9914(pISSN)
  • /
  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

CHARACTERIZATION OF CENTRAL UNITS OF ℤAn

  • Bilgin, Tevfik (DEPARTMENT OF MATHEMATICS FACULTY OF ARTS AND SCIENCES FATIH UNIVERSITY) ;
  • Gorentas, Necat (DEPARTMENT OF MATHEMATICS FACULTY OF ARTS AND SCIENCES YUZUNCU YIL UNIVERSITY) ;
  • Kelebek, I. Gokhan (DEPARTMENT OF MATHEMATICS FACULTY OF ARTS AND SCIENCES FATIH UNIVERSITY)
  • 투고 : 2009.02.26
  • 발행 : 2010.11.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

The structure of V(Ƶ($ZA_n$)) is known when $n\leq6$. If n = 5 or 6, then a complete set of generators of V (Ƶ($ZA_n$)) has been deter-mined. In this study, it was shown that V (Ƶ($ZA_n$)) is trivial when n = 7, 8 or 9 and it is generated by a single unit u when n = 10 or 11: This unit u is characterized explicitly for n = 10 or 11 by using irreducible characters of $A_n$.

키워드

참고문헌

  1. R. Z. Aleev, Higman's central unit theory, units of integral group rings of finite cyclic groups and Fibonacci numbers, Internat. J. Algebra Comput. 4 (1994), no. 3, 309-358. https://doi.org/10.1142/S0218196794000038
  2. R. Z. Aleev, Central elements of integral group rings, Algebra Log. 39 (2000), no. 5, 513-525.
  3. C. W. Curtis and I. Reiner, Representation Theory of Finite Groups and Associative Algebras, Interscience Publishers, a division of John Wiley & Sons, New York-London 1962.
  4. M. Hertweck and E. Jespers, Class-preserving automorphisms and the normalizer property for Blackburn groups, J. Group Theory 12 (2009), no. 1, 157-169. https://doi.org/10.1515/JGT.2008.068
  5. M. Hertweck and W. Kimmerle, Coleman automorphisms of finite groups, Math. Z. 42 (2002), no. 2, 203-215.
  6. E. Jespers, M. M. Parmenter, and S. K. Sehgal, Central units of integral group rings of nilpotent groups, Proc. Amer. Math. Soc. 124 (1996), no. 4, 1007-1012. https://doi.org/10.1090/S0002-9939-96-03398-9
  7. Y. Li and M. M. Parmenter, Central units of the integral group ring $ZA_5$, Proc. Amer. Math. Soc. 125 (1997), no. 1, 61-65. https://doi.org/10.1090/S0002-9939-97-03626-5
  8. Z. F. Patay, Structure of the center of the multiplicative group of a group ring, Visnik Kiiv. Univ. Ser. Mat. Mekh. No. 27 (1985), 90-91, 127.
  9. J. Ritter and S. K. Sehgal, Integral group rings with trivial central units, Proc. Amer. Math. Soc. 108 (1990), no. 2, 327-329. https://doi.org/10.1090/S0002-9939-1990-0994785-7
  10. The GAP Group, GAP - Groups, Algorithms, and Programming, Version 4.4.12, 2008. (http://www.gap-system.org)
  11. Waterloo Maple Inc., Maple, Version 7.00, 2008. (http://www.maplesoft.com)
  12. R. Z. Aleev, Central elements of integral group rings, translation in Algebra and Logic 39 (2000), no. 5, 293-300. https://doi.org/10.1007/BF02681613