Lecture Notes on Bayesian Estimation and Classification
《Lecture Notes on Bayesian Estimation and Classification》 · 第 63–64 页 · Section 3.1「Series and Composition Series」
Let $G$ be an operator group with operator domain $\Omega$. An $\Omega$-series (of finite length) in $G$ is a finite sequence of $\Omega$-subgroups including $1$ and $G$ such that each member of the sequence is a normal subgroup of its successor: thus a series can be written $1=G_0\triangleleft G_1\triangleleft\cdots\triangleleft G_l=G$. […] If $\Omega=\operatorname{Inn}G$, $\operatorname{Aut}G$, or $\operatorname{End}G$, the terms of an $\Omega$-series are normal, characteristic, or fully-invariant in $G$ and we shall speak of a normal series, a characteristic series, or a fully-invariant series.