# Camina group

From Groupprops

This article defines a term that has been used or referenced in a journal article or standard publication, but may not be generally accepted by the mathematical community as a standard term.[SHOW MORE]

This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism

View a complete list of group propertiesVIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

## Definition

### Symbol-free definition

A group is termed a **Camina group** if every coset of the derived subgroup other than the commutator subgroup itself, forms exactly one conjugacy class.

### Definition with symbols

A group is termed a **Camina group** if for every , the coset is a conjugacy class.

## Relation with other properties

### Stronger properties

- Perfect group
- Abelian group
- Extraspecial group:
`For full proof, refer: extraspecial implies Camina`