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Schreier's Refinement Theorem is a result in group theory. Otto Schreir discovered it in 1928, and used it to give an improved proof of the Jordan-Hölder Theorem.
In mathematics, Artin–Schreier theory is a branch of Galois theory, specifically a positive characteristic analogue of Kummer theory, for Galois extensions of degree equal to the characteristic p.
Schreier 定理是群论中关于正规群列的一个定理，它给出了一个群不同的正规群列之间的关系，可用来刻画有限群的结构（Jordan-Hölder 定理）。
rtin{Schreier theorem. In [7] there is an elementary proof (based on the original one, as all known proofs are) under the hypothesis that F has characteristic 0; we essentially reproduce much of that proof below, but ...
Schreier（施赖埃尔）定理：有限群的任意一个词正规群列都可以加细为合成群列。 证：设 G=G_0>G_1>…>G_r=\ {e\} 是 G 的一个次正规群列。
Theorem 27.1 (Nielsen-Schreier). Every subgroup of a free group is free. This follows from the following facts from topology. Lemma 27.2. 1. The fundamental group of any graph Γ is free. 2. The free generators of 1⁄41...
阿廷-施赖埃尔定理 (Artin-Schreier theorem )序域实闭包的序同构性定理.对于任何一个序域 (F,＞)，它所有的实闭包都是互为序同构的，换言之，除序同构不计外，序域的实闭包是惟一确定的.
Schreier–Sims 算法 是计算群论（computational group theory）的一种算法，以数学家 Otto Schreier 和 Charles Sims 的名字命名。 该算法能够在多项式时间内解决诸如找到有限置换群的阶数、查看给定置换是否包含在所给群中等许多问题。
In group theory, a branch of mathematics, the Nielsen–Schreier theorem states that every subgroup of a free group is itself free. [1][2][3] It is named after Jakob Nielsen and Otto Schreier.
This observation led Artin and Schreier to call any field having this property formally real. Any such field can be ordered and, on the other hand, any ordered field is formally real.
