Generalized Camina group

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Definition

Definition with symbols

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

Relation with other properties

Stronger properties

• Abelian group
• Perfect group
• Camina group

Related properties

• Con-Cos group
• Generalized Con-Cos group