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.
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