4 papers · 1 filter
Automatic Quotients of Free Groups
Robert H. Gilman
Automatic groups admitting prefix closed automatic structures with uniqueness are characterized as the quotients of free groups by normal subgroups possessing sets of free generato…
Word Hyperbolic Semigroups
Andrew Duncan, Robert H. Gilman
The study of word hyperbolic groups is a prominent topic in geometric group theory; however word hyperbolic groups are defined by a geometric condition which does not extend natura…
On the Definition of Word Hyperbolic Groups
Robert H. Gilman
Formal languages based on the multiplication tables of finitely generated groups are investigated and used to give a linguistic characterization of word hyperbolic groups.
Combing nilpotent and polycyclic groups
Robert H. Gilman, Derek F. Holt, Sarah Rees
A combing is a set of normal forms for a finitely generated group. This article investigates the language-theoretic and geometric properties of combings for nilpotent and polycycli…