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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

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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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1992-1136226-5
PII: S 0025-5718(1992)1136226-5
Keywords: Modular group algebra, p-group, unit group, generators and relations, presentation of an extension
Article copyright: © Copyright 1992 American Mathematical Society