Geodesic
Unitary Representations of Generalized Symmetric Groups
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 28-38

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper all representations are over the complex field K. The generalized symmetric group S(n, m) of order n!mn is isomorphic to the semi-direct product of the group of n × n diagonal matrices whose rath powers are the unit matrix by the group of all n × n permutation matrices over K. As a permutation group, S(n, m) consists of all permutations of the mn symbols {1, 2, ..., mn} which commute with Obviously, S (1, m) is a cyclic group of order m, while S(n, 1) is the symmetric group of order n!. If ci = (i, n+ i, ..., (m – 1)n+ i) and then {c 1, c 2, ..., cn } generate a normal subgroup Q(n) of order mn and {s 1, s 2, ..., s n...1} generate a subgroup S(n) isomorphic to S(n, 1). 
Puttaswamaiah, B. M. Unitary Representations of Generalized Symmetric Groups. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 28-38. doi: 10.4153/CJM-1969-003-3
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