Torsion-free group with two conjugacy classes

Symbol-free definition
A torsion-free group with two conjugacy classes or aperiodic group with two conjugacy classes is a nontrivial group satisfying these two conditions: it is torsion-free, i.e., no nontrivial element in it has finite order, and it has two conjugacy classes of elements.

Weaker properties

 * Stronger than::Simple torsion-free group

Facts

 * Every torsion-free group is a subgroup of a torsion-free group with two conjugacy classes