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Compression of finite group actions and covariant dimension
- Source :
-
Journal of Algebra . Jul2007, Vol. 313 Issue 1, p268-291. 24p. - Publication Year :
- 2007
-
Abstract
- Abstract: Let G be a finite group and an equivariant morphism of finite-dimensional G-modules. We say that φ is faithful if G acts faithfully on . The covariant dimension of G is the minimum of the dimension of taken over all faithful φ. In this paper we investigate covariant dimension and are able to determine it for abelian groups and to obtain estimates for the symmetric and alternating groups. We also classify groups of covariant dimension less than or equal to 2. A byproduct of our investigations is the existence of a purely transcendental field of definition of degree for a generic field extension of degree . [Copyright &y& Elsevier]
- Subjects :
- *FINITE groups
*GROUP theory
*MODULES (Algebra)
*SET theory
Subjects
Details
- Language :
- English
- ISSN :
- 00218693
- Volume :
- 313
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 25098167
- Full Text :
- https://doi.org/10.1016/j.jalgebra.2006.12.025