This group theory-related article is a stub.
You can help Wikipedia by expanding it.In group theory, especially, in geometric group theory, the class of free-by-cyclic groups have been deeply studied as important examples.
is said to be free-by-cyclic if it has a free normal subgroup
is finitely generated and the quotient is an infinite cyclic group.
Equivalently, we can define a free-by-cyclic group constructively: if
An isomorphism class of a free-by-cyclic group is determined by an outer automorphism.
represent the same outer automorphism, that is,
The study of free-by-cyclic groups is strongly related to that of the attaching outer automorphism.
Among the motivating questions are those concerning their non-positive curvature properties, such as being CAT(0).