>>775 補足
>Jordan–Hölder theorem

これ、下記 Historical Noteで 1869 1889 とあるけど
”Could Jordan Have Proved the Jordan-Hölder Theorem?”
(google訳：ジョルダンはジョルダン＝ヘルダーの定理を証明できたのだろうか？)
とかあって、
たしかに Schreier refinement theorem 1928 を使うとかあるね（年次逆転）
へへー （＾＾

https://proofwiki.org/wiki/Jordan-H%C3%B6lder_Theorem
Jordan-Hölder Theorem
Proof
By the Schreier-Zassenhaus Theorem
Historical Note
The Jordan-Hölder Theorem was proved by Camille Jordan in 1869, and then independently rediscovered by Otto Ludwig Hölder in 1889.

https://en.wikipedia.org/wiki/Schreier_refinement_theorem
Schreier refinement theorem of group theory states that any two subnormal series of subgroups of a given group have equivalent refinements, where two series are equivalent if there is a bijection between their factor groups that sends each factor group to an isomorphic one.

The theorem is named after the Austrian mathematician Otto Schreier who proved it in 1928. It provides an elegant proof of the Jordan–Hölder theorem. It is often proved using the Zassenhaus lemma. Baumslag (2006) gives a short proof by intersecting the terms in one subnormal series with those in the other series.

https://www.jstor.org/stable/40267366
journal article
On Abstraction and the Importance of Asking the Right Research Questions: Could Jordan Have Proved the Jordan-Hölder Theorem?
(google訳：ジョルダンはジョルダン＝ヘルダーの定理を証明できたのだろうか？)
Dirk Schlimm
Erkenntnis (1975-)
Vol. 68, No. 3, Towards a New Epistemology of Mathematics (May, 2008), pp. 409-420 (12 pages)
Published By: Springer Nature