The Modular Group Algebras of P-Groups of Maximal Class

The isomorphism problem for modular group algebras of finite p -groups appears to be still far from a solution (see [ 7 ] for a survey of the existing results). It is therefore of interest to investigate the problem for special classes of groups. The groups we consider here are the p -groups of maximal class, which were extensively studied by Blackburn [ 1 ]. In this paper we solve the modular isomorphism problem for such groups of order not larger than p p +1 , having an abelian maximal subgroup, for odd primes p . What we in fact do is to generalize methods used by Passman [ 5 ] to solve the isomorphism problem for groups of order p 4 . In Passman's paper the case of groups of maximal class is actually the most difficult one.