# Finite-Frattini-realizable group

From Groupprops

BEWARE!This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

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: Frattini subgrouprealizationrelated to the following subgroup-defining function

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 is termed **finite-Frattini-realizable** if there exists a finite group such that where denotes the Frattini subgroup of .

## 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