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

Year 2016, , 61 - 80, 15.05.2016
https://doi.org/10.13069/jacodesmath.79635

Abstract

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.

References

  • [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.
Year 2016, , 61 - 80, 15.05.2016
https://doi.org/10.13069/jacodesmath.79635

Abstract

References

  • [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.
There are 11 citations in total.

Details

Subjects Engineering
Journal Section Articles
Authors

Amanda E. Francis This is me

Stephen P. Humphries This is me

Publication Date May 15, 2016
Published in Issue Year 2016

Cite

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. May 2016;3(2):61-80. doi:10.13069/jacodesmath.79635
Chicago Francis, Amanda E., and Stephen P. Humphries. “Commutative Schur Rings over Symmetric Groups II: The Case N = 6”. Journal of Algebra Combinatorics Discrete Structures and Applications 3, no. 2 (May 2016): 61-80. https://doi.org/10.13069/jacodesmath.79635.
EndNote Francis AE, Humphries SP (May 1, 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 and S. P. Humphries, “Commutative Schur rings over symmetric groups II: The case n = 6”, Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 3, no. 2, pp. 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 (May 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. and Stephen P. Humphries. “Commutative Schur Rings over Symmetric Groups II: The Case N = 6”. Journal of Algebra Combinatorics Discrete Structures and Applications, vol. 3, no. 2, 2016, pp. 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.