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Please use this identifier to cite or link to this item: http://dspace.utalca.cl/handle/1950/4568

Title: On the Similarity Group of Forms of Higher Degree
Authors: Oryan, M.
Issue Date: 1994
Publisher: Academic Press, Inc.
Citation: Journal of Algebra 168 (3): 968-980
Abstract: Let ƒ = ƒ(X) = ƒ(X1,..., Xn,) k[X1,...,Xn] be a non-singular form of degree d ≥ 3 over the field k (where char(k)= 0 or char(k) > d). The similarity group of ƒ, Sk(ƒ) is the subgroup of GLn(k) consisting of all matrices A such that ƒ(AX) = λAƒ(X) for some λA k×. Let Autk(ƒ) denote the automorphism group of ƒ. Identifying k× with the group of scalar matrices in Sk(ƒ), we show using Kummer′s theory of fields that Sk(ƒ)/Autk(ƒ)k× is a finite abelian group of exponent d. We apply this result to give a complete characterization of the similarity group of rational binaries of odd degree.
Description: Oryan M. Univ Talca, Dept Informat & Matemat Aplicada, Talca, Chile.
URI: http://dspace.utalca.cl/handle/1950/4568
ISSN: 0021-8693
Appears in Collections:Artículos en publicaciones ISI - Universidad de Talca

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