[GAP Forum] Group from octonion elements

[Marek Mitros]

Hi,

I have defined octonions over field
o:=OctaveAlgebra(GF(7));

Next create set of some invertible elements belonging to some subalgebra.
And I wanted to see what group is generated by invertible elements in this
subalgebra. Unfortunately I cannot use "Group" function, because I obtain
error "no groups of cyclotomics allowed because of incomatible ^". I am
using GAP version 4.8.8. This subalgebra is associative, because it is
generated by two elements. Therefore invertible elements should form a
group. Do you have any advice or workaround how could I test my group ? I
wanted to use StructureDescription. These are small groups of size
294,336,392 and 686.

gap> g1:=Group([1..5],k->Random(c1i));
#I  no groups of cyclotomics allowed because of incompatible ^
Error, usage: Group(<gen>,...), Group(<gens>), Group(<gens>,<id>) called
from
<function "Group">( <arguments> )
 called from read-eval loop at line 74 of *stdin*
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue
brk> quit;

Regards,
Marek