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

Author: Robert Sandling
Journal: Math. Comp. 59 (1992), 689-701
MSC: Primary 16S34; Secondary 16U60, 20C05, 20D15, 20F05
MathSciNet review: 1136226
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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$, or when $ p = 3$ and the commutator subgroup G' is of order 3. Implementation involves extensive calculation in FG.

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Keywords: Modular group algebra, p-group, unit group, generators and relations, presentation of an extension
Article copyright: © Copyright 1992 American Mathematical Society

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