I had a hard to track down error which eventually relied on sage
permutation groups behave odd in regard to subgroups. A subgroup y of a
subgroup x of g isn't always considered as a subgroup of g. Compare
sage: g = SymmetricGroup(2)
....: x = g.subgroup([])
....: y = x.subgroup([])
....: x == y
....:
False
with
sage: G = gap(g)
....: X = G.Subgroup([])
....: Y = X.Subgroup([])
....: X == Y
....:
True
A probably related strange phenomenon arises with subgroups of g only:
sage: g = SymmetricGroup(3)
....: x = g.subgroup(['(1, 2)', '(2, 3)'])
....: y = g.subgroup(['(1, 3)', '(2, 3)'])
....: x == y; len({x, y})
....:
True
2
On the Gap level, same subgroups given by different generators apparently
get hashed correctly:
sage: gap.eval('G := SymmetricGroup(3);;')
....: gap.eval('U := Subgroup(G, [(1, 2), (2, 3)]);;')
....: gap.eval('V := Subgroup(G, [(1, 3), (2, 3)]);;')
....: gap.eval('Length(Set([U, V]))')
....:
'1'
-- Peter Mueller
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