Holt and Röver proved that finitely generated bounded automata groups have indexed co-word problem. Here we sharpen this result to show they are in fact co-ET0L.
A direct consequence of Gromov's theorem is that if a group has polynomial geodesic growth with respect to some finite generating set then it is virtually nilpotent. However, until now the only examples known were virtually abelian. In this note we furnish an example of a virtually 2-step nilpotent group having polynomial geodesic growth with respect to a certain finite generating set.
Small cancellation groups form an interesting class with many desirable
properties. It is a well-known fact that small cancellation groups are generic;
however, all previously known results of their genericity are asymptotic and
provide no information about "small" group presentations. In this note, we give
closed-form formulas for both lower and upper bounds on the density of small
cancellation presentations, and compare our results with experimental data.
Comment: 18 pages, 12 figures
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.