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The Galois group of f(xr)

Published online by Cambridge University Press:  18 May 2009

S. D. Cohen  and
W. W. Stothers
S. D. Cohen
Affiliation:
Department Of Mathematics, University Of Glasgow, Glasgow G12 8QW, Scotland
W. W. Stothers
Affiliation:
Department Of Mathematics, University Of Glasgow, Glasgow G12 8QW, Scotland
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Let f(x) be an irreducible polynomial of degree n with coefficients in a field L and r be an integer prime to the characteristic of L. The object of this paper is to describe the galois group g of f(xr) over L when the galois group G of f(x) itself over L is either the full symmetric group Snor the alternating group An. We shall call f standard if G = Sn or An with |G|>2.

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 25 , Issue 1 , January 1984 , pp. 75 - 91
Copyright
Copyright © Glasgow Mathematical Journal Trust 1984

References

REFERENCES

1.Carmichael, R., Introduction to the theory of groups of finite order (Dover, 1956).Google Scholar
2.Cohen, S. D., The distribution of the galois groups of integral polynomials, Illinois J. Math. 23 (1979), 135–152.CrossRefGoogle Scholar
3.Fried, M., On a conjecture of Schur, Michigan Math. J. 17 (1970), 41–55.CrossRefGoogle Scholar
4.Huppert, B., Endliche Gruppen I (Springer-Verlag, 1967).CrossRefGoogle Scholar
5.Kaplansky, I., Fields and rings (Chicago, 1969).Google Scholar
6.Wielandt, H., Finite permutation groups (Academic Press, 1964).Google Scholar