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The Modular Group Algebra Problem for Small p-Groups Of Maximal Class

Published online by Cambridge University Press:  20 November 2018

Mohamed A. M. Salim  and
Robert Sandling
Mohamed A. M. Salim
Affiliation:
Mathematics Department Emirates University P.O. Box 17551, Al-Ain United Arab Emirates
Robert Sandling
Affiliation:
Mathematics Department The University Manchester Ml3 9PL England email: rsandling@manchester.ac.uk
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Abstract

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We show that p-groups of maximal class and order p5 are determined by their group algebras over the field of p elements. The most important information requisite for the proof is obtained from a detailed study of the unit group of a quotient algebra of the group algebra, larger than the small group algebra.

Keywords

20C0516S3416U6017B5020D1520F05modular group algebrap-groupisomorphism problemmaximal class
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 48 , Issue 5 , 01 October 1996 , pp. 1064 - 1078
Copyright
Copyright © Canadian Mathematical Society 1996

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