[GAP Forum] Can I safely identify the moved points of PGL(n, 2) with GF(2)^n\0?

[Gordon Royle]

If I use the groups

PGL(n,2)

in GAP, then is it guaranteed that the set permuted by this group can be identified in the obvious fashion with GF(2)^n \ 0?

What I mean is that it would be natural to assign the non-zero vectors in GF(2)^n\0 to integers in the range {1,2,…,2^n-1} simply by treating a 0/1 vector as the binary representation of an integer.

0000001 -> 1
0000010 -> 2
0000011 -> 3

and so on.

>From my experiments, GAP *appears* to behave consistently with this (for example, if I check the stabiliser of [x, y, x ^ y] where x ^ y is bitwise binary XOR, then it is always the correct thing).

But can I rely on it?




Professor Gordon Royle
School of Mathematics and Statistics
University of Western Australia
Gordon.Royle at uwa.edu.au<mailto:Gordon.Royle at uwa.edu.au>