9 papers
Two results on complexities of decision problems of groups
Uri Andrews, Matthew Harrison-Trainor, Meng-Che "Turbo" Ho
We answer two questions on the complexities of decision problems of groups, each related to a classical result. First, C. Miller characterized the complexity of the isomorphism pro…
Rational growth in torus bundle groups of odd trace
Seongjun Choi, Meng-Che "Turbo" Ho, Mark Pengitore
A group is said to hae a rational growth with respect to the generating set if the growth series is a rational polynomial. It was shown by Parry that a subset of torus bundle group…
Word Maps in Finite Simple Groups
William Cocke, Meng-Che "Turbo" Ho
Elements of the free group define interesting maps, known as word maps, on groups. It was previously observed by Lubotzky that every subset of a finite simple group that is closed…
The Probability Distribution of Word Maps on Finite Groups
William Cocke, Meng-Che "Turbo" Ho
Word maps provide a wealth of information about finite groups. We examine the connection between the probability distribution induced by a word map and the underlying structure of…
Finitely Generated Groups Are Universal
Matthew Harrison-Trainor, Meng-Che Ho
Universality has been an important concept in computable structure theory. A class of structures is universal if, informally, for any structure, of any kind, there is…
On optimal Scott sentences of finitely generated algebraic structures
Matthew Harrison-Trainor, Meng-Che Ho
Scott showed that for every countable structure , there is a sentence of the infinitary logic , called a Scott sentence for , whose mo…