Does a group with exponential growth always have a hyperbolic subgroup which has exponential growth?

trefoniu1

trefoniu1

Answered

2022-01-29

Does a group with exponential growth always have a hyperbolic subgroup which has exponential growth?

Answer & Explanation

Jason Olsen

Jason Olsen

Expert

2022-01-30Added 14 answers

There is a heuristic theorem. When the group has a hyperbolic subgroup, by Tits
Addisyn Thompson

Addisyn Thompson

Expert

2022-01-31Added 16 answers

Polycyclic groups that are not virtually nilpotent, such as ⟨x,y,z∣xy=yz,xy=z,zy=yz⟩ have exponential growth, but they have no non-elementary hyperbolic subgroups (i.e. all of their hyperbolic subgroups are virtually cyclic)

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