Hyperfocal 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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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}