LATENT REFERENCES / TAG1
Klein Group
Original title: クライン群
This reference note belongs to Tag1 in Latent References, an archive curated by Keigo Yoshida. Its archive region is Klein bottles · Möbius strips. The note preserves its source text and links so that readers can trace the material behind the 3D map.
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In group theory, a field of mathematics, the Klein four-group is the noncyclic group of smallest order, denoted V or V4. Comprising an identity element and 3 elements of order 2, it is an abelian group with a commutative group operation following the operation table below.
1 i j k
1 1 i j k
i i 1 k j
j j k 1 i
k k j i 1
The Klein four-group is also isomorphic to the direct product of cyclic groups of order 2, ℤ/2ℤ × ℤ/2ℤ, the dihedral group D2, and the normal subgroup {id, (1,2)(3,4), (1,3)(2,4), (1,4)(2,3)} of the alternating group A4.
数学の一分野である群論におけるクラインの四元群とは、巡回群でない位数が最小の群であり、VまたはV4と表記される。 この群は単位元および3つの位数2の元から構成され、以下の演算表に従う可換な群演算を持つアーベル群である。
1 i j k
1 1 i j k
i i 1 k j
j j k 1 i
k k j i 1
また、クラインの四元群は、位数2の巡回群の直積 ℤ/2ℤ × ℤ/2ℤ や二面体群 D2のほか、交代群 A4 の正規部分群 {id, (1,2)(3,4), (1,3)(2,4), (1,4)(2,3)} と同型である。
Source updated 2026-05-24 · Snapshot 2026-10-08
Source links and calculated neighbors
Cosine values measure shared lexical features, not truth, agreement or identical meaning. Original reference links are labeled separately.
- Klein BottleComputed lexical cosine similarity 0.222 · shared title, text, tags and references
- Kleingarten: Allotment GardenComputed lexical cosine similarity 0.171 · shared title, text, tags and references