On Units of Group Algebras of 2-Groups of Maximal Class

Abstract

Abstract We determine the number of elements of order two in the group of normalized units V(𝔽2 G) of the group algebra 𝔽2 G of a 2-group of maximal class over the field 𝔽2 of two elements. As a consequence for the 2-groups G and H of maximal class we have that V(𝔽2 G) and V(𝔽2 H) are isomorphic if and only if G and H are isomorphic.