Geometry & Topology Monographs Hairdressing in Groups: a Survey of Combings and Formal Languages
نویسنده
چکیده
A group is combable if it can be represented by a language of words satisfying a fellow traveller property; an automatic group has a synchronous combing which is a regular language. This article surveys results for combable groups, in particular in the case where the combing is a formal language.
منابع مشابه
Hairdressing in groups: a survey of combings and formal languages
A group is combable if it can be represented by a language of words satisfying a fellow traveller property; an automatic group has a synchronous combing which is a regular language. This article surveys results for combable groups, in particular in the case where the combing is a formal language. AMS Classi cation 20F10, 20-04, 68Q40; 03D40
متن کاملA Note on the Grammar Of Combings
Explicit constructions are given to illustrate the loss of control that ensues when one replaces the regular languages of automatic group theory with larger families of languages. The results of [2] show that one can distinguish between various classes of combable groups by analyzing the grammatical complexity of the combings that the groups admit. That work clarifies the boundaries of automati...
متن کاملA Language Theoretic Analysis of CombingsSarah
A group is combable if it can be represented by a language of words satisfying a fellow traveller property; an automatic group has a synchronous combing which is a regular language. This paper gives a systematic analysis of the properties of groups with combings in various formal language families, and of the closure properties of the associated families of groups; it explores the relationship ...
متن کاملCombing Nilpotent and Polycyclic Groups
The notable exclusions from the family of automatic groups are those nilpotent groups which are not virtually abelian, and the fundamental groups of compact 3-manifolds based on the Nil or Sol geometries. Of these, the 3-manifold groups have been shown by Bridson and Gilman to lie in a family of groups defined by conditions slightly more general than those of automatic groups, that is, to have ...
متن کاملA Remark about Combings of Groups
In the last several years a remarkable interplay between geometry, group theory, and the theory of formal languages has led to developments including the introduction of automatic groups [Ep+], hyperbolic groups [Gro], and geometric and language-theoretic characterizations of finitely generated virtually free groups [MS1] [MS2]. A prime example of such interplay is the study of combings, which ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007