I will discuss the isomorphism problem for modular group algebras of p-groups. The question is: suppose that G and H are p-groups and that their group algebras kG and kH are isomorphic where k is a field of characteristic p. Is it necessary that G and H be isomorphic? It is known that the answer is yes for groups of order 128 (p = 2).

Éamonn O'Brien and I are working on a program to check the groups of order 256. The idea is to use the packages for basic algebras and for finitely presented algebras to create a test for isomorphism of local algebras.