  Using the computational algebra system GAP (http://www.gap-system.org) and
the GAP package LAGUNA (http://www.cs.st-andrews.ac.uk/~alexk/laguna.htm), 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.

Rings and Algebras;Group Theory