groups, the symmetric group is the Coxeter group of type An and occurs as the Weyl group of the general linear group. In combinatorics, the symmetric... 45 KB (5,903 words) - 00:53, 4 March 2024 |
potential applications, from symmetric function theory to quantum chemistry studies of atoms, molecules and solids. The symmetric group Sn has order n!. Its conjugacy... 20 KB (2,677 words) - 17:18, 21 January 2024 |
a group action of G on X as a group homomorphism from G into the symmetric group Sym(X) of all bijections from X to itself. Likewise, a right group action... 45 KB (5,575 words) - 16:39, 3 March 2024 |
the alternating group on n letters and denoted by An or Alt(n). For n > 1, the group An is the commutator subgroup of the symmetric group Sn with index... 17 KB (1,538 words) - 09:24, 20 August 2023 |
generalized symmetric group is the wreath product S(m,n):=Zm≀Sn{\displaystyle S(m,n):=Z_{m}\wr S_{n}} of the cyclic group of order m and the symmetric group of... 3 KB (515 words) - 11:47, 17 October 2022 |
Abel–Ruffini theorem (category Solvable groups) subgroups of its Galois group for expressing this characterization in terms of solvable groups; the proof that the symmetric group is not solvable if its... 28 KB (3,978 words) - 11:40, 20 March 2024 |