[GAP Forum] Naming of Primitive Groups

[Colva Roney-Dougal]

Hi Chris

They are isomorphic groups, so they have the same name. In both cases they’re the alternating and symmetric groups on 5 points; the ones of degree 5 are the natural action, the ones of degree 10 are the actions on unordered pairs. In general any group has multiple primitive actions. 

Best wishes

Colva

On 10 Nov 2013, at 19:54, Chris Jefferson <caj21 at st-andrews.ac.uk> wrote:

> After trying to track down some strange behavior in a program, I was surprised to find the names of the first two primitive groups of size 10:
> 
> gap> PrimitiveGroup(10, 1);
> A(5)
> gap> PrimitiveGroup(10, 2);
> S(5)
> 
> These are, unsurprisingly, the same names as:
> 
> gap> PrimitiveGroup(5,4);
> A(5)
> gap> PrimitiveGroup(5,5);
> S(5)
> 
> Out of curiosity, are these groups related in some non-obvious way, and is there any reason the names of the primitive groups are not unique?
> 
> Chris
> 
> 
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