Adem Relations
The Adem relations for p=2 were conjectured by Wu (1952) and proved by José Adem (1952) and are given by
for all i, j > 0 such that i < 2j. (The binomial coefficients are to be interpreted mod 2.) The Adem relations allow one to write an arbitrary composition of Steenrod squares as a sum of Serre-Cartan basis elements.
For odd p the Adem relations are
for a<pb and
for a≤pb
Read more about this topic: Steenrod Algebra
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“Happy will that house be in which the relations are formed from character; after the highest, and not after the lowest order; the house in which character marries, and not confusion and a miscellany of unavowable motives.”
—Ralph Waldo Emerson (18031882)