Con-Cos group

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

A Con-Cos group is a group $G$ with a normal subgroup $N$ satisfying the following two conditions:

• Any two non-identity elements of $N$ are conjugate in $G$.
• Every non-identity coset of $N$ in $G$ is a conjugacy class in $G$.

Note that if $G$ is an abelian group, we can set $N$ to be the trivial subgroup.

Relation with other properties

Stronger properties

• Abelian group
• Group with two conjugacy classes

Related properties

• Camina group
• Generalized Camina group