[GAP Forum] What does <[ [ 1, 1 ] ]|b*a^-1> mean

[Alexander Hulpke]

Dear Forum, 

On Jun 30, 2013 <rrburns at cox.net>  asked:

> octahedral group using three elements (altho this is not important to to
> questions). I asked GAP for
> gap> asg:=AllSubgroups(g);;
> ## Look at the elements for one of these subgroups
> gap> Elements(asg[24]);
> [ <identity ...>, a*c^-1, <[ [ 1, 1 ] ]|b*a^-1>, c^-1*b, 
>  <[ [ 2, 1 ] ]|c*a^-1>, c*b^-1 ]
> 
> I do not understand the notation, such as, <[ [ 1, 1 ] ]|b*a^-1> 

This is the element b*a, stored via a straight line program. (This representation happens as the calculation of subgroups uses some nontrivial homomorphisms, for larger groups it saves memory.)
These elements behave fr all practical purposes just like the normal words in finitely presented groups.

Regards,

    Alexander Hulpke