Lecture Notes on Bayesian Estimation and Classification
《Lecture Notes on Bayesian Estimation and Classification》 · 第 358 页 · Section 12.1「Locally Nilpotent Groups」，小节「Ascendant Subgroups」
By an ascending series in a group $G$ we shall mean a set of subgroups $\{H_\alpha\mid\alpha<\beta\}$ indexed by ordinals less than an ordinal $\beta$ such that: (a) $H_{\alpha_1}\le H_{\alpha_2}$ if $\alpha_1\le\alpha_2$; (b) $H_0=1$ and $G=\bigcup_{\alpha<\beta}H_\alpha$; (c) $H_\alpha\triangleleft H_{\alpha+1}$; (d) $H_\lambda=\bigcup_{\alpha<\lambda}H_\alpha$ if $\lambda$ is a limit ordinal. […] A subgroup which occurs in some ascending series of a group $G$ is called an ascendant subgroup; this is an evident generalization of a subnormal subgroup.