Steenrod reduced power

Summary

For an odd prime $p$, the Steenrod reduced powers $P^i$ are cohomology operations on mod $p$ singular cohomology that raise degree by $2i(p-1)$. They play for odd primes the role that the Steenrod squares play for the prime $2$. Together with the Bockstein homomorphism they generate all stable mod $p$ cohomology operations. They detect maps that ordinary cohomology groups and cup products cannot see.