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

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.

Key Words:

• Group algebra
• Group of units
• Isomorphism
• Element of order two

2001 Mathematics Subject Classifications:

• Primary 16A46
• 16A26
• 20C05
• Secondary 19A22

Acknowledgment

The research was supported by OTKA, grants No. T037202 and No. T043034.

Notes

^#Communicated by I. Shestakov.