# Focal series of a subgroup

From Groupprops

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This article is about a definition in group theory that is standard among the group theory community (or sub-community that dabbles in such things) but is not very basic or common for people outside.VIEW: Definitions built on this | Facts about this: (factscloselyrelated to Focal series of a subgroup, all facts related to Focal series of a subgroup) |Survey articles about this | Survey articles about definitions built on this

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## Definition

Suppose is a subgroup of a group . The **focal series** of in is a series where we define:

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In other words, each member of the series is the focal subgroup of its predecessor. The focal subgroup is defined as:

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A subgroup whose focal series terminates at the trivial subgroup is termed a hyperfocal subgroup.