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Theorems · Theorem · group theory

AddSubgroup.nsmul_relIndex_mem

∀ {G : Type u_6} [inst : AddGroup G] (H : AddSubgroup G) [H.Normal] {K : AddSubgroup G} {g : G},
  g ∈ K → H.relIndex K • g ∈ H
Defined in
Mathlib.GroupTheory.OrderOfElement
Cited by
1 results in Mathlib
Foundations
Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddGroupAddSubgroup.Normal
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Around this declaration

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NumberField.exists_nat_ne_zero_exists_integer_mul_eq_and_absNorm_span_eq_pow · cited by 1NumberField.exists_nat_ne…AddGroup · cited by 4410AddGroupAddSubgroup · cited by 3232AddSubgroupAddSubgroup.Normal · cited by 183AddSubgroup.NormalAddSubgroup.addSubgroupOf · cited by 87AddSubgroup.addSubgroupOfAddSubgroup.relIndex · cited by 67AddSubgroup.relIndexAddSubgroup.nsmul_index_mem · cited by 3AddSubgroup.nsmul_index_m…AddSubgroup.nsmul_relIndex_memCITED BYCITES

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