[過去ﾛｸﾞ] 現代数学の系譜 工学物理雑談 古典ガロア理論も読む78 (1002ﾚｽ)
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384(1): 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE 2019/11/02(土)11:26 ID:ZLEqKHqI(15/18) AAS
>>375
>　PSL(2,q)はP1(Fq)への推移的な作用で

外部ﾘﾝｸ:en.wikipedia.org
Projective space
(抜粋)
Morphisms
Injective linear maps T ∈ L(V, W) between two vector spaces V and W over the same field k induce mappings of the corresponding projective spaces P(V) → P(W) via:
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385(1): 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE 2019/11/02(土)11:27 ID:ZLEqKHqI(16/18) AAS
>>384

つづき

Finite projective spaces and planes
Further information on finite projective planes: Projective plane § Finite projective planes

For finite projective spaces of dimension at least three, Wedderburn's theorem implies that the division ring over which the projective space is defined must be a finite field, GF(q), whose order
(that is, number of elements) is q (a prime power). A finite projective space defined over such a finite field has q + 1 points on a line, so the two concepts of order coincide. Notationally, PG(n, GF(q)) is usually written as PG(n, q).

All finite fields of the same order are isomorphic, so, up to isomorphism, there is only one finite projective space for each dimension greater than or equal to three, over a given finite field.
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