Presentations for unit groups of modular group algebras of groups of order 16

Abstract

For a p-group G and the field F of p elements, let V denote the group of normalized units of the group algebra FG. Generators and relations are provided for V for each group G of order dividing 16. The presentations are sufficiently concise to permit transcription for machine calculation with V. Some applications are described. A theoretical method for obtaining presentations for V is developed. It is most effective when p = 2 p = 2 , or when p = 3 p = 3 and the commutator subgroup G’ is of order 3. Implementation involves extensive calculation in FG.