Linear relations between roots of polynomials

• Autorzy: Kurt Girstmair
• Języki publikacji: EN

Kategorie tematyczne

• 12F10: Separable extensions, Galois theory
• 12E05: Polynomials (irreducibility, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1999
• Tom: 89
• Numer: 1
• Strony: 53-96

Daty

wydano

1999

otrzymano

1998-09-18

poprawiono

1998-12-07

Twórcy

autor

Kurt Girstmair

• Institut für Mathematik, Universität Innsbruck, Technikerstr. 25/7, A-6020 Innsbruck, Austria

Bibliografia

• [1] G. Baron, M. Drmota and M. Skałba, Polynomial relations between polynomial roots, J. Algebra 177 (1995), 827-846.
• [2] T. Breuer and K. Lux, The multiplicity-free permutation characters of the sporadic simple groups and their automorphism groups, Comm. Algebra 24 (1996), 2293-2316.
• [3] P. J. Cameron, Finite permutation groups and finite simple groups, Bull. London Math. Soc. 13 (1981), 1-22.
• [4] J. W. S. Cassels and A. Fröhlich (eds.), Algebraic Number Theory, Academic Press, London, 1967.
• [5] J. H. Conway et al., Atlas of Finite Groups, Clarendon Press, Oxford, 1985.
• [6] C. W. Curtis and I. Reiner, Methods of Representation Theory, Vol. II, Wiley, New York, 1987.
• [7] J. D. Dixon, Polynomials with nontrivial relations between their roots, Acta Arith. 82 (1997), 293-302.
• [8] J. D. Dixon and B. Mortimer, Permutation Groups, Springer, New York, 1996.
• [9] M. Drmota and M. Skałba, On multiplicative and linear independence of polynomial roots, in: Contributions to General Algebra 7, D. Dorninger et al. (eds.), Hölder-Pichler-Tempsky, Wien, and Teubner, Stuttgart, 1991, 127-135
• [10] M. Drmota and M. Skałba, Relations between polynomial roots, Acta Arith. 71 (1995), 65-77.
• [11] K. Girstmair, Linear dependence of zeros of polynomials and construction of primitive elements, Manuscripta Math. 39 (1982), 81-97.
• [12] B. Huppert, Endliche Gruppen I, Springer, Berlin, 1967; reprint 1979.
• [13] B. Huppert and N. Blackburn, Finite Groups III, Springer, Berlin, 1982.
• [14] V. A. Kurbatov, Galois extensions of prime degree and their primitive elements, Soviet Math. (Iz. VUZ) 21 (1977), 49-53.
• [15] M. W. Liebeck and J. Saxl, The primitive permutation groups of odd degree, J. London Math. Soc. (2) 31 (1985), 250-264.
• [16] G. Malle und B. H. Matzat, Realisierung von Gruppen $PSL₂(𝔽_p)$ als Galoisgruppen über ℚ, Math. Ann. 272 (1985), 549-565.
• [17] H. P. Schlickewei and S. A. Stepanov, Algorithms to construct normal bases of cyclic number fields, J. Number Theory 44 (1993), 30-40.
• [18] J. P. Serre, Linear Representations of Finite Groups, Springer, New York, 1977.
• [19] C. J. Smyth, Additive and multiplicative relations connecting conjugate algebraic numbers, J. Number Theory 23 (1986), 243-254.
• [20] H. Wielandt, Finite Permutation Groups, Academic Press, New York, 1964.