# Difference between revisions of "Subnormal subgroup"

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(New page: '''Subnormal subgroup''': A subgroup of a group such that there is an ascending chain of subgroups, starting from that subgroup to the whole group, with each member normal in the next. Suc...) |
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Primary subject wiki entry: [[Groupprops:Subnormal subgroup]] | Primary subject wiki entry: [[Groupprops:Subnormal subgroup]] | ||

− | Related terms: [[Groupprops:Normal subgroup]], [[Groupprops:2-subnormal subgroup]], [[Groupprops:3-subnormal subgroup]], [[Groupprops:Ascendant subgroup]], [[Groupprops:Descendant subgroup]], [[Groupprops:Serial subgroup]], [[Groupprops:Subnormal series]], [[Groupprops:Normal series]] | + | Related terms: [[Groupprops:Normal subgroup|Normal subgroup]], [[Groupprops:2-subnormal subgroup|2-subnormal subgroup]], [[Groupprops:3-subnormal subgroup|3-subnormal subgroup]], [[Groupprops:Ascendant subgroup|ascendant subgroup]], [[Groupprops:Descendant subgroup|descendant subgroup]], [[Groupprops:Serial subgroup|serial subgroup]], [[Groupprops:Subnormal series|subnormal series]], [[Groupprops:Normal series|normal series]] |

## Latest revision as of 15:14, 8 November 2008

**Subnormal subgroup**: A subgroup of a group such that there is an ascending chain of subgroups, starting from that subgroup to the whole group, with each member normal in the next. Such an ascending chain is termed a subnormal series.

A -subnormal subgroup is a subgroup for which there exists a subnormal series of length at most . Particular examples are (normal subgroup), (2-subnormal subgroup), (3-subnormal subgroup).

Primary subject wiki entry: Groupprops:Subnormal subgroup

Related terms: Normal subgroup, 2-subnormal subgroup, 3-subnormal subgroup, ascendant subgroup, descendant subgroup, serial subgroup, subnormal series, normal series