Abstract
Let K be a field of characteristic 0 and φ a rational function in variables x 1, …, x n over K. Let S n We denote the permutation group of n elements. We can assign to φ the stabilizer of φ, i.e., the group
For example, if φ is a symmetric function, then G φ = S n , whereas if φ =∑a i x i , where the numbers a 1,…, a n are distinct, then G φ contains only the identity permutation.
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© 2004 Springer-Verlag Berlin Heidelberg
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Prasolov, V.V. (2004). Galois Theory. In: Polynomials. Algorithms and Computation in Mathematics, vol 11. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03980-5_5
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DOI: https://doi.org/10.1007/978-3-642-03980-5_5
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-03979-9
Online ISBN: 978-3-642-03980-5
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