[GAP Forum] About the elements of abstract group SmallGroup(8,1).

[Hongyi Zhao]

Hi GAP team,

For the abstract group SmallGroup(8,1), I noticed the following
related information:

gap> g:=SmallGroup(8,1);
<pc group of size 8 with 3 generators>
gap> Elements(g);
[ <identity> of ..., f1, f2, f3, f1*f2, f1*f3, f2*f3, f1*f2*f3 ]
gap> SmallGeneratingSet(g);
[ f1 ]
gap> StructureDescription(g);
"C8"

As you can see, it's a cyclic group of order 8. So, I wonder why the
elements don't look like this:

[ <identity> of ..., f1, f1^2, f1^3, f1^4, f1^5, f1^6, f1^7 ]

Regards,
-- 
Assoc. Prof. Hongsheng Zhao <hongyi.zhao at gmail.com>
Theory and Simulation of Materials
Hebei Vocational University of Technology and Engineering
No. 473, Quannan West Street, Xindu District, Xingtai, Hebei province