The finitely presented intermediate-growth conjecture
A group has intermediate growth when its growth is faster than every polynomial and slower than every exponential function.
Finitely presented intermediate-growth conjecture. There are no finitely presented groups of intermediate growth.
The existence of finitely presented groups of intermediate growth is described as a major open problem, and the source says the answer is believed to be negative.
References
Primary source
Rostislav Grigorchuk and Igor Pak, “Groups of Intermediate Growth: an Introduction for Beginners”, arXiv:math/0607384 (2006).
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