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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

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