Alex Bishop

Alex Bishop
The University of Sydney · School of Mathematics and Statistics

About

7
Publications
173
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5
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Introduction

Publications

Publications (7)
Article
We show that the geodesic growth function of any finitely generated virtually abelian group is either polynomial or exponential; and that the geodesic growth series is holonomic, and rational in the polynomial growth case. In addition, we show that the language of geodesics is blind multicounter.
Article
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 u...
Preprint
Full-text available
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 respe...
Preprint
Full-text available
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...
Preprint
Full-text available
We show that no finitely generated virtually abelian group has intermediate geodesic growth, and that the language of geodesics for such a group is blind multicounter.
Preprint
Full-text available
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.

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