Definition:Normal Series/Infinite
< Definition:Normal Series(Redirected from Definition:Infinite Normal Series)
Jump to navigation
Jump to search
Definition
A normal series may or may not terminate at either end:
- $\cdots \stackrel {\phi_{i - 1} } {\longrightarrow} H_{i - 1} \stackrel {\phi_i} {\longrightarrow} H_i \stackrel {\phi_{i + 1} } {\longrightarrow} H_{i + 1} \stackrel {\phi_{i + 2} } {\longrightarrow} \cdots$
Such a series is referred to as an infinite normal series.
The context will determine which end, if either, it terminates.
Sources
- 1967: George McCarty: Topology: An Introduction with Application to Topological Groups ... (previous) ... (next): Chapter $\text{II}$: Groups: Problem $\text{FF}$