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University of Arizona

1. McShane, Janet Marie. Computation of polynomial invariants of finite groups.

Degree: 1992, University of Arizona

If G is a finite subgroup of GL(n,K), K a field of characteristic 0, it is well known that the algebra I of polynomial invariants of G is Cohen-Macaulay. Consequently I has a subalgebra J of Krull dimension n so that I is a free J-module of finite rank. A sequence (f₁,...,f(n);g₁,...,g(m)) of homogeneous invariants is a Cohen-Macaulay (or CM) basis if J = K[f₁,...,f(n)] and {g₁,...,g(m)} is a basis for I as a J-module. We discuss an algorithm, and an implementation using the systems GAP and Maple, for the calculation of CM-bases. Advisors/Committee Members: Fan, Paul (committeemember), Gay, David (committeemember), Flaschka, Hermann (committeemember), Laetsch, Theodore (committeemember).

Subjects/Keywords: Dissertations, Academic.; Mathematics.

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

McShane, J. M. (1992). Computation of polynomial invariants of finite groups. (Doctoral Dissertation). University of Arizona. Retrieved from http://hdl.handle.net/10150/186000

Chicago Manual of Style (16th Edition):

McShane, Janet Marie. “Computation of polynomial invariants of finite groups. ” 1992. Doctoral Dissertation, University of Arizona. Accessed January 16, 2021. http://hdl.handle.net/10150/186000.

MLA Handbook (7th Edition):

McShane, Janet Marie. “Computation of polynomial invariants of finite groups. ” 1992. Web. 16 Jan 2021.

Vancouver:

McShane JM. Computation of polynomial invariants of finite groups. [Internet] [Doctoral dissertation]. University of Arizona; 1992. [cited 2021 Jan 16]. Available from: http://hdl.handle.net/10150/186000.

Council of Science Editors:

McShane JM. Computation of polynomial invariants of finite groups. [Doctoral Dissertation]. University of Arizona; 1992. Available from: http://hdl.handle.net/10150/186000

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