Free-by-cyclic group

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In group theory, a group G is said to be free-by-cyclic if it has a free normal subgroup F such that the quotient group

G / F

is cyclic.

In other words, G is free-by-cyclic if it can be expressed as a group extension of a free group by a cyclic group (NB there are two conventions for 'by').

If F is a finitely generated group we say that G is (finitely generated free)-by-cyclic (or (f.g. free)-by-cyclic).

[edit] References

• A. Martino and E. Ventura (2004), The Conjugacy Problem for Free-by-Cyclic Groups. Preprint from the Centre de Recerca Matemàtica, Barcelona, Catalonia, Spain.