Camina group

Symbol-free definition
A group is termed a Camina group if every coset of the defining ingredient::derived subgroup other than the commutator subgroup itself, forms exactly one defining ingredient::conjugacy class.

Definition with symbols
A group $$G$$ is termed a Camina group if for every $$g \notin [G,G]$$, the coset $$g[G,G]$$ is a conjugacy class.

Stronger properties

 * Weaker than::Perfect group
 * Weaker than::Abelian group
 * Weaker than::Extraspecial group:

Weaker properties

 * Stronger than::Generalized Camina group

Related properties

 * Con-Cos group
 * Generalized Con-Cos group

Facts

 * Alternating groups are Camina groups
 * Dihedral groups are Camina groups for degree odd or at most four