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The modular group algebra problem for groups of order p5

Part of: Rings and algebras arising under various constructions Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

Mohamed A. M. Salim  and
Robert Sandling
Mohamed A. M. Salim
Affiliation:
Mathematics Dept. Emirates UniversityP. O. Box 17551, Al-Ain, United Arab Emirates
Robert Sandling
Affiliation:
Mathematics Dept. The UniversityManchester M13 9PLEngland e-mail: rsandling@manchester.ac.uk
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Abstract

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We show that p-groups of order p5 are determined by their group algebras over the field of p elements. Many cases have been dealt with in earlier work of ourselves and others. The only case whose details remain to be given here is that of groups of nilpotency class 3 for p odd.

Keywords

modular group algebrap-groupisomorphism problem

MSC classification

Secondary: 20C05: Group rings of finite groups and their modules 16S34: Group rings , Laurent polynomial rings 20D15: Nilpotent groups, $p$-groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 61 , Issue 2 , October 1996 , pp. 229 - 237
Copyright
Copyright © Australian Mathematical Society 1996

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