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Commutative Schur rings over symmetric groups II: The case n = 6

Yıl 2016, Cilt: 3 Sayı: 2, 61 - 80, 15.05.2016
https://doi.org/10.13069/jacodesmath.79635

Öz

We determine the commutative Schur rings over $S_6$ that contain the sum of all the transpositions in
$S_6$. There are eight such types (up to conjugacy), of which four have the set of all the transpositions
as a principal set of the Schur ring.

Kaynakça

  • [1] W. Bosma, J. Cannon, Magma handbook, University of Sydney, 1993.
  • [2] C. W. Curtis, Pioneers of Representation Theory: Frobenius, Burnside, Schur, and Brauer. Vol. 15. American Mathematical Soc., 1999.
  • [3] S. A. Evdokimov, I. N. Ponomarenko, On a family of Schur rings over a finite cyclic group (Russian), Algebra i Analiz. 13(3) (2001) 139–154; translation in St. Petersburg Math. J. 13(3) (2002) 441–451.
  • [4] S. P. Humphries, Commutative Schur rings over symmetric groups, J. Algebraic Combin. 42(4) (2015) 971–997.
  • [5] S. P. Humphries, K. W. Johnson, A. Misseldine, Commutative Schur rings of maximal dimension, Comm. Algebra. 43(12) (2015) 5298–5327.
  • [6] K. H. Leung, S. H. Man, On Schur rings over cyclic groups, Israel J. Math. 106(1) (1998) 251–267.
  • [7] K. H. Leung, S. H. Man, On Schur rings over cyclic groups, II, J. Algebra. 183(2) (1996) 273–285.
  • [8] M. E. Muzychuk, On the structure of basic sets of Schur rings over cyclic groups, J. Algebra. 169(2) (1994) 655–678.
  • [9] M. Muzychuk, I. Ponomarenko, Schur rings, European J. Combin. 30(6) (2009) 1526–1539.
  • [10] I. Schur, Zur Theorie der einfach transitiven Permutationsgruppen, 1933.
  • [11] H. Wielandt, Finite permutation groups, Academic Press, 2014.
Yıl 2016, Cilt: 3 Sayı: 2, 61 - 80, 15.05.2016
https://doi.org/10.13069/jacodesmath.79635

Öz

Kaynakça

  • [1] W. Bosma, J. Cannon, Magma handbook, University of Sydney, 1993.
  • [2] C. W. Curtis, Pioneers of Representation Theory: Frobenius, Burnside, Schur, and Brauer. Vol. 15. American Mathematical Soc., 1999.
  • [3] S. A. Evdokimov, I. N. Ponomarenko, On a family of Schur rings over a finite cyclic group (Russian), Algebra i Analiz. 13(3) (2001) 139–154; translation in St. Petersburg Math. J. 13(3) (2002) 441–451.
  • [4] S. P. Humphries, Commutative Schur rings over symmetric groups, J. Algebraic Combin. 42(4) (2015) 971–997.
  • [5] S. P. Humphries, K. W. Johnson, A. Misseldine, Commutative Schur rings of maximal dimension, Comm. Algebra. 43(12) (2015) 5298–5327.
  • [6] K. H. Leung, S. H. Man, On Schur rings over cyclic groups, Israel J. Math. 106(1) (1998) 251–267.
  • [7] K. H. Leung, S. H. Man, On Schur rings over cyclic groups, II, J. Algebra. 183(2) (1996) 273–285.
  • [8] M. E. Muzychuk, On the structure of basic sets of Schur rings over cyclic groups, J. Algebra. 169(2) (1994) 655–678.
  • [9] M. Muzychuk, I. Ponomarenko, Schur rings, European J. Combin. 30(6) (2009) 1526–1539.
  • [10] I. Schur, Zur Theorie der einfach transitiven Permutationsgruppen, 1933.
  • [11] H. Wielandt, Finite permutation groups, Academic Press, 2014.
Toplam 11 adet kaynakça vardır.

Ayrıntılar

Konular Mühendislik
Bölüm Makaleler
Yazarlar

Amanda E. Francis Bu kişi benim

Stephen P. Humphries Bu kişi benim

Yayımlanma Tarihi 15 Mayıs 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 3 Sayı: 2

Kaynak Göster

APA Francis, A. E., & Humphries, S. P. (2016). Commutative Schur rings over symmetric groups II: The case n = 6. Journal of Algebra Combinatorics Discrete Structures and Applications, 3(2), 61-80. https://doi.org/10.13069/jacodesmath.79635
AMA Francis AE, Humphries SP. Commutative Schur rings over symmetric groups II: The case n = 6. Journal of Algebra Combinatorics Discrete Structures and Applications. Mayıs 2016;3(2):61-80. doi:10.13069/jacodesmath.79635
Chicago Francis, Amanda E., ve Stephen P. Humphries. “Commutative Schur Rings over Symmetric Groups II: The Case N = 6”. Journal of Algebra Combinatorics Discrete Structures and Applications 3, sy. 2 (Mayıs 2016): 61-80. https://doi.org/10.13069/jacodesmath.79635.
EndNote Francis AE, Humphries SP (01 Mayıs 2016) Commutative Schur rings over symmetric groups II: The case n = 6. Journal of Algebra Combinatorics Discrete Structures and Applications 3 2 61–80.
IEEE A. E. Francis ve S. P. Humphries, “Commutative Schur rings over symmetric groups II: The case n = 6”, Journal of Algebra Combinatorics Discrete Structures and Applications, c. 3, sy. 2, ss. 61–80, 2016, doi: 10.13069/jacodesmath.79635.
ISNAD Francis, Amanda E. - Humphries, Stephen P. “Commutative Schur Rings over Symmetric Groups II: The Case N = 6”. Journal of Algebra Combinatorics Discrete Structures and Applications 3/2 (Mayıs 2016), 61-80. https://doi.org/10.13069/jacodesmath.79635.
JAMA Francis AE, Humphries SP. Commutative Schur rings over symmetric groups II: The case n = 6. Journal of Algebra Combinatorics Discrete Structures and Applications. 2016;3:61–80.
MLA Francis, Amanda E. ve Stephen P. Humphries. “Commutative Schur Rings over Symmetric Groups II: The Case N = 6”. Journal of Algebra Combinatorics Discrete Structures and Applications, c. 3, sy. 2, 2016, ss. 61-80, doi:10.13069/jacodesmath.79635.
Vancouver Francis AE, Humphries SP. Commutative Schur rings over symmetric groups II: The case n = 6. Journal of Algebra Combinatorics Discrete Structures and Applications. 2016;3(2):61-80.