Kraft, Hanspeter and Kohls, Martin. (2010) Degree bounds for separating invariants. Mathematical research letters, Vol. 17. pp. 11711182.

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Abstract
If V is a representation of a linear algebraic group G, a set S of Ginvariant regular functions on V is called separating if the following holds: If two elements v,v' from V can be separated by an invariant function, then there is an f from S such that f(v) is different from f(v'). It is known that there always exist finite separating sets. Moreover, if the group G is finite, then the invariant functions of degree ≤ G form a separating set. We show that for a nonfinite linear algebraic group G such an upper bound for the degrees of a separating set does not exist. If G is finite, we define b(G) to be the minimal number d such that for every Gmodule V there is a separating set of degree less or equal to d. We show that for a subgroup H of G we have b(H) ≤ b(G) ≤ [G:H] b(H), and that b(G) ≤ b(G/H) b(H) in case H is normal. Moreover, we calculate b(G) for some specific finite groups.
Faculties and Departments:  05 Faculty of Science > Departement Mathematik und Informatik > Ehemalige Einheiten Mathematik & Informatik > Algebra (Kraft) 

UniBasel Contributors:  Kraft, Hanspeter 
Item Type:  Article, refereed 
Article Subtype:  Research Article 
Publisher:  International Press 
ISSN:  10732780 
Note:  Publication type according to Uni Basel Research Database: Journal article 
Language:  English 
Last Modified:  31 Dec 2015 10:49 
Deposited On:  08 Jun 2012 06:48 
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