Cyclic Reduced Powers of Cohomology Classes.

In a previous paper' we have shown that each homology class c of the symmetric group Sn provides a topologically invariant operation defined for each cohomology class u of a complex, and it gives a cohomology class un/c called the nth power reduced by c. In this paper we state properties of the simplest of these, namely, those provided by cycles c lying on the cyclic subgroup of Sn of order n. We shall continue with the notation and numbering of the previous paper. 4. Homology Groups of the Cyclic Group.-Let r be the cyclic group of permutations of the factors of Xn, and T its generatorwhich increases the index of the factor by 1 mod n. In the group ring Z(r), set