Symmetric Groups

Some articles on symmetric groups, symmetric group, group:

Boundedly Generated Group - Free Groups Are Not Boundedly Generated - Symmetric Groups
... The symmetric group Sn can be generated by two elements, a 2-cycle and an n-cycle, so that it is a quotient group of F2 ...
Symmetric Group
... The symmetric group on a finite set X is the group whose elements are all bijective functions from X to X and whose group operation is that of function composition ... The symmetric group of degree n is the symmetric group on the set X = { 1, 2.. ... The symmetric group on a set X is denoted in various ways including SX, ΣX, and Sym(X) ...
Symmetric Group - Low Degree Groups
... See also Representation theory of the symmetric group#Special cases The low-degree symmetric groups have simpler and exceptional structure, and often must be treated separately ... Sym(0) and Sym(1) The symmetric groups on the empty set and the singleton set are trivial, which corresponds to 0! = 1! = 1 ... In this case the alternating group agrees with the symmetric group, rather than being an index 2 subgroup, and the sign map is trivial ...

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