Commutative Schur rings over symmetric groups II: The case n = 6
Commutative Schur rings over symmetric groups II: The case n = 6
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.
Keywords:
Schur ring, Conjugacy class Symmetric group, Group algebra,
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- [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.
- Başlangıç: 2015
- Yayıncı: İrfan ŞİAP
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