Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-13T01:06:37.754Z Has data issue: false hasContentIssue false
  • English
  • Français

The Characterisation of Modular Group Algebras Having Unit Groups of Nilpotency Class 3

Published online by Cambridge University Press:  20 November 2018

M. Anwar Rao  and
Robert Sandling
M. Anwar Rao
Affiliation:
Mathematics Department, The University, Manchester M13 9PL, England, e-mail:[email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The unit group of the modular group algebra of a finite p-group in characteristic p is nilpotent. The p-groups for which it is of nilpotency class 3 were determined in work of Coleman, Passman, Shalev and Mann when p ≥ 3. We resolve the p = 2 case here which completes the classification.

Keywords

16U6016S3420C0520C2020D15modular group algebrap-groupnilpotency class 3unit group
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 38 , Issue 1 , 01 March 1995 , pp. 112 - 116
Copyright
Copyright © Canadian Mathematical Society 1995

References

1. Baginski, C., Groups of units of modular group algebras, Proc. Amer. Math. Soc. 101(1987), 619–624.Google Scholar
2. Cannon, J. J., An introduction to the group theory language Cayley, Computational group theory, Academic Press, London, 1984, 145–183.Google Scholar
3. Coleman, D. B. and Passman, D. S., Units in modular group rings, Proc. Amer. Math. Soc. 25(1970), 510– 512.Google Scholar
4. Du, X., The centers of a radical ring, Canad. Math. Bull. (2) 35(1992), 174–179.Google Scholar
5. Gupta, N. and Levin, F., On the Lie ideals of a ring, J. Algebra 81(1983), 225–231.Google Scholar
6. Huppert, B., Endliche Gruppen I, Springer, Berlin, 1967.Google Scholar
7. Laue, H., On the associated Lie ring and the adjoint group of a radical ring, Canad. Math. Bull. (2) 27( 1984), 215–222.Google Scholar
8. Mann, A. and Shalev, A., The nilpotency class of the unit group of a modular group algebra II, Israel J. Math. 70(1990), 267–277.Google Scholar
9. Rao, M. A., Computer calculations of presentations of the unit groups of the modular group algebras of the groups of order dividing 32, Ph.D. thesis, Manchester Univ., 1993.Google Scholar
10. Sandling, R., Presentations for unit groups of modular group algebras of groups of order 16, Math. Comp. 59(1992), 689–701.Google Scholar
11. Shalev, A., The nilpotency class of the unit group of a modular group algebra I, Israel J. Math. 70(1990), 257–266.Google Scholar
12. Shalev, A., The nilpotency class of the unit group of a modular group algebra III, Arch. Math. (Basel) 60(1993), 136–145.Google Scholar