Generalized Camina group

Definition with symbols
A group $$G$$ is termed a generalized Camina group if the following holds. Let $$Z(G)$$ be the defining ingredient::center of $$G$$ and $$[G,G]$$ be the defining ingredient::commutator subgroup of $$G$$. Then, for $$g \notin [G,G]Z(G)$$, the coset $$g[G,G]$$ is a single defining ingredient::conjugacy class.

Stronger properties

 * Weaker than::Abelian group
 * Weaker than::Perfect group
 * Weaker than::Camina group

Related properties

 * Con-Cos group
 * Generalized Con-Cos group