Hyperfocal subgroup
From Groupprops
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: (facts closely related to Hyperfocal subgroup, all facts related to Hyperfocal subgroup) |Survey articles about this | Survey articles about definitions built on this
VIEW RELATED: Analogues of this | Variations of this | Opposites of this |
View a list of other standard non-basic definitions
This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]
Definition
A subgroup of a group is termed a hyperfocal subgroup if its focal series terminates in finitely many steps at the trivial subgroup.
Facts
- Hall and hyperfocal implies retract: If a Hall subgroup of a finite group is also hyperfocal, then it is a retract: it possesses a normal complement.
References
Journal references
- Focal series in finite groups by Donald Gordon Higman, , Volume 5, Page 477 - 497(Year 1953): ^{}^{More info}