image of a subgroup #2201
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image of a subgroup #2201
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Alizter
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I've also absorbed |
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I also added some more comments and reorganised some things in |
jdchristensen
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Alizter
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jdchristensen
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Jan 21, 2025
<!-- ps-id: a131ab0f-2a90-4e3c-86d0-37a687960d7b --> Signed-off-by: Ali Caglayan <[email protected]>
Signed-off-by: Ali Caglayan <[email protected]>
Signed-off-by: Ali Caglayan <[email protected]>
Signed-off-by: Ali Caglayan <[email protected]>
Signed-off-by: Ali Caglayan <[email protected]>
Signed-off-by: Ali Caglayan <[email protected]>
Signed-off-by: Ali Caglayan <[email protected]>
Signed-off-by: Ali Caglayan <[email protected]>
Signed-off-by: Ali Caglayan <[email protected]>
Signed-off-by: Ali Caglayan <[email protected]>
Alizter
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I've just force pushed to resolve the conflicts. The latest commit was new which flipped the direction of the kernel equivalence and made the sigma types easier to see. |
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Here we introduce the image of a subgroup under a group homomorphism. This is obviously a generalisation of what exists in
Image.vhowever sincesubgroup_group (maximal_subgroup G)isn't definitionallyG, it makes working with the "standard image" a little bit more finicky, so I deemed it was not worth merging them.I therefore opted to introduce this version specifically for subgroups and proved some standard properties about it.
We show that images are adjoint to preimages and images of normal subgroups under a surjective homomorphism are normal.