Source: wikibot/free-by-cyclic-group
= Free-by-cyclic group
{wiki=Free-by-cyclic_group}
A *free-by-cyclic group* is a specific type of group that can be thought of as a combination of two structures: a free group and a cyclic group. More formally, a free-by-cyclic group is a group \\( G \\) that can be expressed in the form: \\\[ G = F \\rtimes C \\\] where \\( F \\) is a free group and \\( C \\) is a cyclic group.