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Let ( l , m ) is an ordered pair of positive integers ORDER l = { 1,2 , ... , l } , m = { 1,2 , ... , m } , s = L X m = { (i, j) | i ∈ l, j ∈ m}. said set s symmetry group with s ml . s subset I called admissible set , if ( i , j ) ∈ I , then ( i ' j ) I , ? i ' ∈ l \\ { i } , s ( l , m ) is set by to Sml the allowable subset of s mappings to allow a subset of those replacement subgroups constituted , the sub- group is called generalized symmetry group of type ( l , m ) . generalized symmetric group S ( l , m ) is isomorphic to the symmetric group Sl and Sm spined SL ? Sm in this paper, the following : (1) S ( l is given , m) a set generating element and define relationships ; ( 2) to determine the function of the length of the S ( l , m ) , l ( w ) ; ( 3 ) determines the length of the polynomial S ( l , m ) LG ( t ) .
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