On 09/02/2018 09:47, Simon Brandhorst wrote:

Return whether the group was defined as a subgroup of a bigger
group.

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This description is very unclear anyway. See also #24535 for ambiguities
concerning group comparisons.
For me there are two relevant concepts
1) whether H is a subgroup of G, for example
sage: G = PermutationGroup([ [4,3,2,1], [2,1,4,3] ])
sage: H = PermutationGroup([ [4,3,2,1] ])
sage: H.is_subgroup(G)
True
Here I did *not* defined H as a subgroup of G (so the above description
does not apply). Note that in order for this comparison to make sense,
G and H must be subgroups of a same ambient group (here
SymmetricGroup(4)). But there is no such thing as an .ambient_group
method.
2) whether G contains a subgroup isomorphic to H. In this situation no
need to have a common ambient group
I think that more generally discussing and fixing the semantic of group
comparisons (and more generally algebraic structures) would be a good
idea... and the behavior would ideally be coherent among all of Sage!
Vincent
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