= Steenrod reduced power
{c}
{title2=$P^i:H^q(X;\mathbb F_p)\to H^{q+2i(p-1)}(X;\mathbb F_p)$}
= Steenrod power
{c}
{synonym}
For odd prime $p$, the reduced powers are natural <stable cohomology operations>. They satisfy $P^0=1$, the <Cartan formula>, and the instability conditions $P^i a=0$ for $2i>|a|$ and $P^i a=a^p$ for $|a|=2i$. In particular, a degree-two class has $P^1x=x^p$ and no higher nonzero reduced power. Stability lets these operations detect distinctions between suspensions whose additive cohomology and cup products agree.
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