Frattini-embedded normal subgroup
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Contents
Definition
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
Left transiter
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.
References
- 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