Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-22T14:55:36.981Z Has data issue: false hasContentIssue false
  • English
  • Français

Resolvents Of Certain Linear Groups In a Finite Field

Published online by Cambridge University Press:  20 November 2018

L. Carlitz
L. Carlitz*
Affiliation:
Duke University, Durham, North Carolina
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let Fq = GF(q) denote the finite field of order q = pn, where p is a prime. Consider the group Γ of linear transformations

(1.1) x' = (ax + b)//(cx + d)

with coefficients a, b, c, d ∊ Fq and of determinant 1. The order of Γ is ½q(q2 − 1) or q(q2 − 1) according as q is odd or even, i.e., according as p > 2 or p = 2.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 8 , 1956 , pp. 568 - 579
Copyright
Copyright © Canadian Mathematical Society 1956

References

1. Dickson, L. E., An invariantive investigation of irreducible binary modular forms, Trans. Amer. Math. Soc. 12 (1911), 1–8.Google Scholar
2. Dickson, L. E., Linear Groups (Leipzig, 1901).Google Scholar
3. Dickson, L. E., Modern Algebraic Theories (New York, 1923).Google Scholar
4. Fricke, R., Die elliptische Funktionen und ihre Anwendungen, II (Leipzig and Berlin, 1922).Google Scholar
5. Fricke, R., Lehrbuch der Algebra, II (Braunschweig, 1926).Google Scholar
6. Garrett, J. R., Normal equations and resolvents in fields of characteristic p, Duke Math. J. 18 (1951), 373–384.Google Scholar
7. Klein, F., Vorlesungen über das Ikosaeder und die Auflösung der Gleichungen vom fünften Grade (Leipzig, 1884).Google Scholar
8. Rutherford, D. E., Modular Invariants, Cambridge Tracts in Mathematics and Mathematical Physics, No. 27 (Cambridge, 1932).Google Scholar