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
is much, much slower than
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.