Focal series of a subgroup
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.
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Suppose is a subgroup of a group . The focal series of in is a series where we define:
In other words, each member of the series is the focal subgroup of its predecessor. The focal subgroup is defined as:
A subgroup whose focal series terminates at the trivial subgroup is termed a hyperfocal subgroup.