Computing the invariant ring of a finite group
نویسندگان
چکیده
منابع مشابه
Generating a Noetherian Normalization of the Invariant Ring of a Finite Group
We improve Kemper's algorithm for the computation of a Noetherian normalization of the invariant ring of a nite group. The new algorithm, which still works over arbitrary coeecient elds, no longer relies on algorithms for primary decomposition.
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We consider invariants of a finite group G related to the number of random (independent, uniformly distributed) conjugacy classes which are required to generate it. These invariants are intuitively related to problems of Galois theory. We find group-theoretic expressions for them and investigate their values both theoretically and numerically.
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Article history: Received 21 October 2010 Available online 24 October 2011 Communicated by Ronald Solomon Dedicated to Bob Guralnick in honor of his 60th birthday
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A subset S of a finite group G invariably generates G if G = 〈sg(s) | s ∈ S〉 for each choice of g(s) ∈ G, s ∈ S. We give a tight upper bound on the minimal size of an invariable generating set for an arbitrary finite group G. In response to a question in [KZ] we also bound the size of a randomly chosen set of elements of G that is likely to generate G invariably. Along the way we prove that eve...
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ژورنال
عنوان ژورنال: Journal of Software for Algebra and Geometry
سال: 2013
ISSN: 1948-7916,1948-7916
DOI: 10.2140/jsag.2013.5.15