Original Articles

Permutation actions of the symmetric group Sn on the Groups Zn m and Zn m


Let m and n be positive integers. Let Z m = {0, 1, …, m − 1} be the cyclic group of order m and Z n m be the direct product of n copies of Z m . We discuss here results which give the orbits of permutation actions of the symmetric group Sn on the group Z n m and on the set Irr(Z n m ) of irreducible characters of N from a combinatorial point of view. We also consider the actions of Sn on a factor group Z n m of Z n m and on Irr(Z n m ). Such information are useful in the construction of the Fischer-Clifford matrices of group extensions, in this case the generalized symmetric groups B(m,n) and some related groups, which may arise as subgroups of simple groups [5].

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