Linear relations between roots of polynomials

Kurt Girstmair

Acta Arithmetica (1999)

  • Volume: 89, Issue: 1, page 53-96
  • ISSN: 0065-1036

How to cite

top

Kurt Girstmair. "Linear relations between roots of polynomials." Acta Arithmetica 89.1 (1999): 53-96. <http://eudml.org/doc/207259>.

@article{KurtGirstmair1999,
author = {Kurt Girstmair},
journal = {Acta Arithmetica},
keywords = {linear relations; polynomials; Galois group; permutation representation},
language = {eng},
number = {1},
pages = {53-96},
title = {Linear relations between roots of polynomials},
url = {http://eudml.org/doc/207259},
volume = {89},
year = {1999},
}

TY - JOUR
AU - Kurt Girstmair
TI - Linear relations between roots of polynomials
JO - Acta Arithmetica
PY - 1999
VL - 89
IS - 1
SP - 53
EP - 96
LA - eng
KW - linear relations; polynomials; Galois group; permutation representation
UR - http://eudml.org/doc/207259
ER -

References

top
  1. [1] G. Baron, M. Drmota and M. Skałba, Polynomial relations between polynomial roots, J. Algebra 177 (1995), 827-846. Zbl0835.12003
  2. [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. Zbl0855.20013
  3. [3] P. J. Cameron, Finite permutation groups and finite simple groups, Bull. London Math. Soc. 13 (1981), 1-22. Zbl0463.20003
  4. [4] J. W. S. Cassels and A. Fröhlich (eds.), Algebraic Number Theory, Academic Press, London, 1967. 
  5. [5] J. H. Conway et al., Atlas of Finite Groups, Clarendon Press, Oxford, 1985. 
  6. [6] C. W. Curtis and I. Reiner, Methods of Representation Theory, Vol. II, Wiley, New York, 1987. 
  7. [7] J. D. Dixon, Polynomials with nontrivial relations between their roots, Acta Arith. 82 (1997), 293-302. Zbl0881.12001
  8. [8] J. D. Dixon and B. Mortimer, Permutation Groups, Springer, New York, 1996. Zbl0951.20001
  9. [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. [10] M. Drmota and M. Skałba, Relations between polynomial roots, Acta Arith. 71 (1995), 65-77. 
  11. [11] K. Girstmair, Linear dependence of zeros of polynomials and construction of primitive elements, Manuscripta Math. 39 (1982), 81-97. Zbl0514.12010
  12. [12] B. Huppert, Endliche Gruppen I, Springer, Berlin, 1967; reprint 1979. Zbl0217.07201
  13. [13] B. Huppert and N. Blackburn, Finite Groups III, Springer, Berlin, 1982. Zbl0514.20002
  14. [14] V. A. Kurbatov, Galois extensions of prime degree and their primitive elements, Soviet Math. (Iz. VUZ) 21 (1977), 49-53. 
  15. [15] M. W. Liebeck and J. Saxl, The primitive permutation groups of odd degree, J. London Math. Soc. (2) 31 (1985), 250-264. Zbl0573.20004
  16. [16] G. Malle und B. H. Matzat, Realisierung von Gruppen P S L ( p ) als Galoisgruppen über ℚ, Math. Ann. 272 (1985), 549-565. 
  17. [17] H. P. Schlickewei and S. A. Stepanov, Algorithms to construct normal bases of cyclic number fields, J. Number Theory 44 (1993), 30-40. Zbl0780.11053
  18. [18] J. P. Serre, Linear Representations of Finite Groups, Springer, New York, 1977. Zbl0355.20006
  19. [19] C. J. Smyth, Additive and multiplicative relations connecting conjugate algebraic numbers, J. Number Theory 23 (1986), 243-254. Zbl0586.12001
  20. [20] H. Wielandt, Finite Permutation Groups, Academic Press, New York, 1964. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.