Abstract. Using the computational algebra system GAP and the package LAGUNA, we checked that all 2-groups of order not greater than 32 are determined by normalized unit groups of their modular group algebras over the field of two elements.

AMS Subject Classification (1991): 16S34, 20C05

Keyword(s): modular group algebras

Received July 10, 2006. (Registered under 5953/2009.)