In mathematics, a Pontryagin cohomology operation is a cohomology operation taking cohomology classes in H<sup>2n</sup>(X,Z/p<sup>r</sup>Z) to H<sup>2pn</sup>(X,Z/p<sup>r+1</sup>Z) for some prime number p. When p=2 these operations were introduced by and were named Pontrjagin squares by (with the term "Pontryagin square" also being used). They were generalized to arbitrary primes by .