normal subgroup

(group theory) A subgroup H of a group G that is invariant under conjugation; that is, for all elements h of H and for all elements g in G, the element ghg⁻¹ is in H.

Japanese Meaning

正規部分群：群論において、群 G の部分群 H が任意の g ∈ G と h ∈ H に対し、ghg⁻¹ ∈ H となる場合、H は G の正規部分群と呼ばれる。

What is this buttons?

If every conjugate of an element of H lies in H, then H is a normal subgroup of G.

Google Translation / DeepL Translation

もしHの任意の元のすべての共役がHに含まれるなら、HはGの正規部分群です。

Details

Sense（1）

(group theory) A subgroup H of a group G that is invariant under conjugation; that is, for all elements h of H and for all elements g in G, the element ghg⁻¹ is in H.

normal subgroups

（ plural ）

Details

normal subgroup

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