• Thumbnail for Symmetric group
    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
  • Thumbnail for Affine symmetric group
    The affine symmetric groups are a family of mathematical structures that describe the symmetries of the number line and the regular triangular tiling of...
    71 KB (9,866 words) - 14:17, 15 January 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
  • Thumbnail for Group action
    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
  • Thumbnail for Permutation group
    permutation group is a subgroup of a symmetric group; that is, its elements are permutations of a given set. It is thus a subset of a symmetric group that is...
    23 KB (3,234 words) - 23:32, 28 March 2024
  • Thumbnail for Alternating group
    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
  • Thumbnail for Dihedral group of order 6
    dihedral group of degree 3 and order 6. It equals the symmetric group S3. It is also the smallest non-abelian group. This page illustrates many group concepts...
    18 KB (2,596 words) - 00:21, 27 July 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
  • Thumbnail for Braid group
    i<j\leq n}. This is invariant under the symmetric group, and Y{\displaystyle Y} is the quotient by the symmetric group of the non-excluded n{\displaystyle...
    36 KB (4,654 words) - 16:18, 4 January 2024