Ivan Shishkin, Birch Grove

Normal subgroup

Definition / General algebra / Stub

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A subgroup NN of a group GG is called a normal subgroup of GG if, for every g∈Gg \in G,
gN=Ng.gN = Ng.

Practice this concept with exercises

  • Soit GG un groupe et HH un sous-groupe de GG.
    Montrer que HH est distingué dans GG si et seulement si
    ∀h,k∈G,  hk∈H  ⟹  kh∈H.\forall h,k\in G,\; hk\in H \implies kh\in H.

    Open exerciseDifficulty 36/100 · 1 solution · 0 hints
Problems using this concept (2)
Normal subgroups of SO3(R)\mathrm{SO}_3(\mathbb{R})Quotient of a group and subgroup
Problems using this concept (spoiler) (0)

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