improvements to trivial group #2186
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Signed-off-by: Ali Caglayan <alizter@gmail.com> <!-- ps-id: 806836eb-8793-4452-af1a-11ceb893c83a -->
This was referenced Jan 4, 2025
Signed-off-by: Ali Caglayan <alizter@gmail.com>
jdchristensen
approved these changes
Jan 4, 2025
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First, we rename
IsTrivialSubgrouptoIsTrivialGroup.maximal_subgroupis now a coercion, which means we can writeIsTrivialGroup Gfor a subgroupG, therefore dropping thesubseemed appropriate.Next we simplify the definition by only requiring a map into the trivial group, which corresponds to a subgroup inclusion. The reverse inclusion is trivial, and is stated for completeness. It didn't need to be part of the data.
Finally we show that a group is trivial iff it is isomorphic to the trivial group. Seems negligible on paper, but some details need to be provided.