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A Geometric Model for the Generalized Symmetric Group

Published online by Cambridge University Press:  20 November 2018

Norman W. Johnson
Norman W. Johnson*
Affiliation:
University of Toronto
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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.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 3 , Issue 2 , 01 May 1960 , pp. 133 - 142
Copyright
Copyright © Canadian Mathematical Society 1960

References

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