TY - JOUR TT - Commutative Schur rings over symmetric groups II: The case n = 6 AU - Francis, Amanda E. AU - Humphries, Stephen P. PY - 2016 DA - May DO - 10.13069/jacodesmath.79635 JF - Journal of Algebra Combinatorics Discrete Structures and Applications PB - iPeak Academy WT - DergiPark SN - 2148-838X SP - 61 EP - 80 VL - 3 IS - 2 KW - Schur ring KW - Conjugacy class KW - Symmetric group KW - Group algebra N2 - 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 transpositionsas a principal set of the Schur ring. CR - [1] W. Bosma, J. Cannon, Magma handbook, University of Sydney, 1993. CR - [2] C. W. Curtis, Pioneers of Representation Theory: Frobenius, Burnside, Schur, and Brauer. Vol. 15. American Mathematical Soc., 1999. CR - [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. CR - [4] S. P. Humphries, Commutative Schur rings over symmetric groups, J. Algebraic Combin. 42(4) (2015) 971–997. CR - [5] S. P. Humphries, K. W. Johnson, A. Misseldine, Commutative Schur rings of maximal dimension, Comm. Algebra. 43(12) (2015) 5298–5327. CR - [6] K. H. Leung, S. H. Man, On Schur rings over cyclic groups, Israel J. Math. 106(1) (1998) 251–267. CR - [7] K. H. Leung, S. H. Man, On Schur rings over cyclic groups, II, J. Algebra. 183(2) (1996) 273–285. CR - [8] M. E. Muzychuk, On the structure of basic sets of Schur rings over cyclic groups, J. Algebra. 169(2) (1994) 655–678. CR - [9] M. Muzychuk, I. Ponomarenko, Schur rings, European J. Combin. 30(6) (2009) 1526–1539. CR - [10] I. Schur, Zur Theorie der einfach transitiven Permutationsgruppen, 1933. CR - [11] H. Wielandt, Finite permutation groups, Academic Press, 2014. UR - https://doi.org/10.13069/jacodesmath.79635 L1 - https://dergipark.org.tr/en/download/article-file/267716 ER -