Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-16T15:26:06.723Z Has data issue: false hasContentIssue false

Modules over infinite nilpotent groups

Published online by Cambridge University Press:  09 April 2009

J. R. J. Groves
Affiliation:
Department of Mathematics and Statistics, University of Melbourne, VIC 3010, Australia 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 paper discusses modules over free nilpotent groups and demonstrates that faithful modules are more restricted than might appear at first glance. Some discussion is also made of applying the techniques more generally.

Keywords

MSC classification

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2001

References

[1]Brookes, C. J. B., ‘Stabilisers of injective modules over nilpotent groups’, in: Group theory proceedings of the 1987 Singapore conference (Eds. Cheng, Kai Nah, Leong, Yu Kiang) (de Gruyter, Berlin, New York, 1989) pp. 275291.Google Scholar
[2]Brookes, C. J. B., ‘Non-commutative toric geometry’, in: Groups St Andrews 1997 in Bath, I (Eds. Campbell, C. M., Robertson, E. F., Ruskuc, N., Smith, G. C.) (Cambridge University Press, 1999) pp. 176194.CrossRefGoogle Scholar
[3]Brookes, C. J. B., ‘Crossed products and finitely presented groups’, J. Group Theory 3 (2000), 433444.CrossRefGoogle Scholar
[4]Brookes, C. J. B. and Groves, J. R. J., ‘Modules over nilpotent group rings’, J. London Math. Soc. (2) 52 (1995), 467481.Google Scholar
[5]Brookes, C. J. B. and Groves, J. R. J., ‘Modules over crossed products of a division ring with an abelian group I’, J. Algebra 229 (2000), 2554.CrossRefGoogle Scholar
[6]Brookes, C. J. B. and Groves, J. R. J., ‘Some infinite soluble groups, their modules and the arithmeticity of associated automorphism groups’, in preparation.Google Scholar
[7]Brown, Kenneth S., Cohomology of groups (Springer, New York, 1988).Google Scholar
[8]Megnus, Wilhelm, Karrass, Abraham and Solitar, Donald, Combinatorial group theory (Dover Publ., New York, 1976).Google Scholar
[9]Passman, D. S., The algebraic structure of group rings (John Wiley, New York, 1977).Google Scholar
[10]Ure, Dugal, Finitely presented nilpotent groups and Lie algebras (Ph.D. Thesis, University of Melbourne, 2001).Google Scholar