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 [...

{\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...

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

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

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

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

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...

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