[GAP Forum] calculating maximal blocks

[Will Chen]

Dear all,

Suppose M is a permutation group. What exactly is the behavior of
MaximalBlocks?

It seems that when M is primitive, MaximalBlocks(M, MovedPoints(M)) returns
the trivial block system with 1 block (containing everything). Is this
always the case?

On the other hand, when M is not primitive MaximalBlocks seems to return
something nontrivial. In this case, is it always guaranteed to return a
nontrivial block system on which the action of M is primitive?

These two different behaviors seem confusing to me. I would have expected
MaximalBlock to give the trivial block system of singletons in the
primitive case.

Separately, is there a simple way to compute a maximal block of minimal
cardinality?

Thank you,

- Will

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William Chen
Member, School of Mathematics
Institute for Advanced Study
Princeton, NJ, 08540
oxeimon at gmail.com