Abstract
Let p be a prime. In this survey we attempt to explain how the presence of Steenrod operations in the mod - p cohomology ring H(G;Fp) of a group G allows to understand qualitative features of this ring, at least for a large class of groups including all nite groups but also many discrete groups like arithmetic groups, mapping class groups and automorphism groups of free groups. We will also discuss how the general theory can be applied to do actual calculations.
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