Question regarding PGL groups

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Article #179

#179

From: Andrea A. Pietracaprina
Date: Mon, 11 Jan 1993 15:05

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Hello,
does anyone know a solution to the following problem?

Let PGL(2,k) be the Projective General Linear group of 2 X 2 matrices
with entries from the finite field with k elements, where k is a
prime power. Let q be an even prime power and n and integer > 2. Consider
the quotient

                  PGL(2,q^n) / PGL(2,q)

As known, it consists of [(q^n+1) q^n (q^n-1)] / [(q+1) q (q-1)] elements,
i.e., cosets of PGL(2,q). Is there an ordering of these cosets such that
given an index i it is easy to determine the i-th coset? By easy I mean
requiring *a few* operations in the field.

I would greately appreciate suggestions and/or pointers to the literature.
Thanks in advance.

andrea pietracaprina

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From: aap@cs.brown.edu (Andrea A. Pietracaprina)
Subject: Question regarding PGL groups
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