Fix a prime p, and let A be the polynomial part of the dual Steenrod algebra. The Frobenius map on A induces the Steenrod operation (P) over tilde (0) on cohomology, and in this paper, we investigate this operation. We point out that if p = 2, then for any element in the cohomology of A, if one applies (P) over tilde (0) enough times, the resulting element is nilpotent. We conjecture that the same is true at odd primes, and that "enough times" should be "once."
展开▼
