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Finite-Frattini-realizable group
From Groupprops
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BEWARE! This term is nonstandard and is being used locally within the wiki. For its use outside the wiki, please define the term when using it. If you are aware of an equivalent standard term, please leave a comment on the talk page
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This article defines a property that can be evaluated for finite groups (and hence, a particular kind of group property)
View other properties of finite groups OR View all group properties
This term is related to the problem of realization related to the following subgroup-defining function: Frattini subgroup
Realization problems are usually about which groups can be realized as subgroups/quotients related to a subgroup-defining function.
View other terminology related to realization problems for Frattini subgroup OR View facts related to them
Definition
Symbol-free definition
A finite group is termed finite-Frattini-realizable if it can be realized as the Frattini subgroup of some finite group.
Definition with symbols
A finite group G is termed finite-Frattini-realizable if there exists a finite group K such that 
where Φ(K) denotes the Frattini subgroup of K.
Relation with other properties
Weaker properties
- Finite ACIC-group: For full proof, refer: Frattini subgroup is ACIC
- Finite nilpotent group
- Frattini-realizable group: A group that can be realized as the Frattini subgroup of a not necessarily finite group
- Finite-(Frattini-embedded normal)-realizable group
