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Theorems · Theorem · group theory

solvable_of_ker_le_range

Deprecated since 2026-07-16Use Group.isSolvable_of_ker_le_range instead.

∀ {G : Type u_1} [inst : Group G] {G' : Type u_3} {G'' : Type u_4} [inst_1 : Group G'] [inst_2 : Group G'']
  (f : G' →* G) (g : G →* G''),
  g.ker ≤ f.range → ∀ [hG' : Group.IsSolvable G'] [hG'' : Group.IsSolvable G''], Group.IsSolvable G

Alias of Group.isSolvable_of_ker_le_range.

Defined in
Mathlib.GroupTheory.Solvable
Cited by
0 results in Mathlib
Foundations
Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
GroupGroupGroupGroup.IsSolvableGroup.IsSolvable
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Group · cited by 6238GroupMonoidHom · cited by 3629MonoidHomSubgroup · cited by 3593SubgroupMonoidHom.range · cited by 314MonoidHom.rangeMonoidHom.ker · cited by 212MonoidHom.kerGroup.IsSolvable · cited by 46Group.IsSolvableGroup.isSolvable_of_ker_le_range · cited by 5Group.isSolvable_of_ker_l…solvable_of_ker_le_rangeCITED BYCITES

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