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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
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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

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