Geodesic
A Geometric Model for the Generalized Symmetric Group
Canadian mathematical bulletin, Tome 3 (1960) no. 2, pp. 133-142

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The generalized symmetric group S(n, m) consists of all permutations of mn symbols commutative with Since each cycle Qi = (1i 2i ... mi) is of order m, there are mn permutations within the n cycles, generating an invariant subgroup Q of order mn. Also, there are n! ways of permuting the cycles among themselves, by transformations where i1, i2, ..., in are the symbols 1, 2, ..., n in some order [5, p. 39]. The permutations W* form a subgroup Sn* of order n!, isomorphic to the symmetric group Sn. 
Johnson, Norman W. A Geometric Model for the Generalized Symmetric Group. Canadian mathematical bulletin, Tome 3 (1960) no. 2, pp. 133-142. doi: 10.4153/CMB-1960-016-7
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