[GAP Forum] Can I safely identify the moved points of PGL(n, 2) with GF(2)^n\0?
Gordon Royle
gordon.royle at uwa.edu.au
Wed Mar 13 07:52:30 GMT 2013
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>
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