### Some articles on *symmetric groups, symmetric group, group*:

Boundedly Generated Group - Free Groups Are Not Boundedly Generated -

... The

**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

... 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

... 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 ...### Famous quotes containing the word groups:

“Writers and politicians are natural rivals. Both *groups* try to make the world in their own images; they fight for the same territory.”

—Salman Rushdie (b. 1947)