Dear Gap-Forum,

Laurent Bartholdi asked:

i defined a few rather largish groups (order 3^238, acting on 3^6
points), and noticed quite
surprisingly that the test
gap> D=E;
true
is much, much slower than
gap> Index(D,E)=1;
true
how come?????

For permutation groups, `Index(D,E)' will check whether E is a subset of D
and then compare the sizes.

`D=E' checks whether the generating sets are the same or whether the
sizes are the same and whether all generators of D are in E.

Without knowing the exact way how the groups were created, I have to guess a
bit, but this is what I suspect happens in your example:

You created `E' as a `Subgroup' of `D'. In this case, the subset
test required for `Index' is very quick (being a `Subgroup' implies subset),
and so only the sizes need to be compared.
Checking whether the generators of D lie in E requires sifting them all
through a stabilizer chain, which takes the time.

If you deem this explanation unlikely, let me know more about your example
and I'll have another look.

Best,

Alexander Hulpke