composition series

《代数学引论》 · 第 87 页

如果一个次正规子群列 (1) 的每个因子群 $G_{i-1}/G_i$ 都是单群，则 (1) 称为一个合成群列。

由 admin 提交

《Abstract Algebra》 · 第 102-103 页 · Section 3.4「Composition Series and the Hölder Program」，Definition

In a group $G$ a sequence of subgroups $1=N_0\trianglelefteq N_1\trianglelefteq\cdots\trianglelefteq N_k=G$ is called a composition series if $N_i\trianglelefteq N_{i+1}$ and $N_{i+1}/N_i$ is a simple group, $0\leq i\leq k-1$. If the above sequence is a composition series, the quotient groups $N_{i+1}/N_i$ are called composition factors of $G$.