The isomorphism problem for graded algebras and its application to mod-p cohomology rings of small p-groups

摘要

The mod-p cohomology ring of a non-trivial finite p-group is an infinitedimensional, finitely presented graded unital algebra over the field with pelements, with generators in positive degrees. We describe an effectivealgorithm to test if two such algebras are graded isomorphic. As application,we determine all graded isomorphisms between the mod-p cohomology rings of allp-groups of order at most 100.