Frattini-embedded normal subgroup
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 with symbols
A normal subgroup of a group is termed Frattini-embedded or Frattini-imbedded if for every proper subgroup of , . When is a finite group, or more generally, when every proper subgroup of is contained in a maximal subgroup, then this condition is equivalent to saying that is contained in the Frattini subgroup of .
Effect of property operators
Any characteristic subgroup of a Frattini-embedded normal subgroup is Frattini-embedded normal. It's not clear whether characteristicity is precisely the left transiter of the property of being Frattini-embedded normal.
- An Essay on Frattini Imbedded Normal Subgroups by R. Baer, Comm. Pure Appl. Math. 26, 609--658 (1973)
- On Frattini Imbedded Normal Subgroups by Martin Newell