and the symmetric group of order n. For m = 1 , {\displaystyle m=1,} the generalized symmetric group is exactly the ordinary symmetric group: S ( 1 ,...

History of group theory Signed symmetric group and Generalized symmetric group Symmetry in quantum mechanics § Exchange symmetry Symmetric inverse semigroup...

nonzero entry must be 1, in a generalized permutation matrix the nonzero entry can be any nonzero value. An example of a generalized permutation matrix is [...

either the whole symmetric group Sn or the alternating group An. It was first proved by Camille Jordan. The statement can be generalized to the case that...

{\displaystyle \mathbb {Z} _{2}} the hyperoctahedral group is a special case of a generalized symmetric group. The smallest non-trivial wreath product is Z 2...

The affine symmetric groups are a family of mathematical structures that describe the symmetries of the number line and the regular triangular tiling of...

compact Lie groups. Flag manifolds can be symmetric spaces. Over the complex numbers, the corresponding flag manifolds are the Hermitian symmetric spaces....

the groups whose Sylow 2-subgroups are generalized quaternion cannot be simple. Another terminology reserves the name "generalized quaternion group" for...

symmetries of the edges. The latter two factors are examples of generalized symmetric groups, which are themselves examples of wreath products. (There is...

Riemannian symmetric spaces that are not Riemannian symmetric may be constructed as quotients of Riemannian symmetric spaces by discrete groups of isometries...

uniform polytopes. ———— (1960-05-01). "A Geometric Model for the Generalized Symmetric Group". Canadian Mathematical Bulletin. 3 (2): 133–142. doi:10.4153/CMB-1960-016-7...

are referred to below as "symmetric" and "asymmetric"; however, this is not a standard nomenclature. The symmetric generalized normal distribution, also...

group, O(p, q) is the Lie group of all linear transformations of an n-dimensional real vector space that leave invariant a nondegenerate, symmetric bilinear...

The group G(m, 1, n) is the generalized symmetric group; equivalently, it is the wreath product of the symmetric group Sym(n) by a cyclic group of order...

groups. It is possible to find many examples of generalized Kac–Moody algebras using the following principle: anything that looks like a generalized Kac–Moody...

under the control of domestic units and hence is marked by generalized reciprocity (or generalized exchange). Wealth objects – by their nature from outside...

structure which simultaneously generalizes certain aspects of flag manifolds, finite projective planes, and Riemannian symmetric spaces. Buildings were initially...

Riemannian symmetric space from real manifolds to complex manifolds. Every Hermitian symmetric space is a homogeneous space for its isometry group and has...

generally, any generalized dihedral group is metabelian, as it has an abelian normal subgroup of index 2. If F is a field, the group of affine maps x...

that the order (the number of elements) of the symmetric group Sn is n!. A cyclic group Zn is a group all of whose elements are powers of a particular...

group SO(n), and is called the rotation group of the figure. In a discrete symmetry group, the points symmetric to a given point do not accumulate toward...

theorem, essentially says that any group is in fact just a subgroup of a symmetric group (up to isomorphism). In the symmetric semigroup (of all transformations)...

real and imaginary parts: the real part is symmetric (orthogonal), and the imaginary part is skew-symmetric (symplectic)—and these are related by the complex...

The dual graph of this embedding is a symmetric 6-regular graph with 12 vertices and 36 edges. The other symmetric embedding of the Nauru graph has six...

generalized quaternion groups. Any group such that all Sylow subgroups are cyclic is called a Z-group, and in particular must be a metacyclic group:...

u2), a symmetric graph without isolated vertices must also be vertex-transitive. Since the definition above maps one edge to another, a symmetric graph...

is symmetric if it can be divided into two or more identical pieces that are arranged in an organized fashion. This means that an object is symmetric if...

The name "generalized braid group" arises from the fact that, in the special case W = S n {\displaystyle W=S_{n}} is the symmetric group, the associated...

inverse semigroup, called the symmetric inverse semigroup (actually a monoid) on X. The conventional notation for the symmetric inverse semigroup on a set...

needed] The Gelfand property is often satisfied by symmetric pairs. A pair (G, K) is called a symmetric pair if there exists an involutive automorphism θ...