From automatic structures to automatic groups

Details From automatic structures to automatic groups From automatic structures to automatic groups

2011-07-19

arxiv.org/abs/1107.3645v2

Mathematics

Group Theory

Added references, corrected typos

Scientific paper

In this paper we introduce the concept of a Cayley graph automatic group (CGA group or graph automatic group, for short) which generalizes the standard notion of an automatic group. Like the usual automatic groups graph automatic ones enjoy many nice properties: these group are invariant under the change of generators, they are closed under direct and free products, certain types of amalgamated products, and finite extensions. Furthermore, the Word Problem in graph automatic groups is decidable in quadratic time. However, the class of graph automatic groups is much wider then the class of automatic groups. For example, we prove that all finitely generated 2-nilpotent groups and Baumslag-Solitar groups B(1,n) are graph automatic, as well as many other metabelian groups.

Affiliated with

Also associated with

No associations

Rating

From automatic structures to automatic groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with From automatic structures to automatic groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and From automatic structures to automatic groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-514303