Name
Abstract | ||
|---|---|---|
This text, Chapter 23 in the "AutoMathA" handbook, is devoted to the study of
rational subsets of groups, with particular emphasis on the automata-theoretic
approach to finitely generated subgroups of free groups. Indeed, Stallings'
construction, associating a finite inverse automaton with every such subgroup,
inaugurated a complete rewriting of free group algorithmics, with connections
to other fields such as topology or dynamics.
Another important vector in the chapter is the fundamental Benois' Theorem,
characterizing rational subsets of free groups. The theorem and its
consequences really explain why language theory can be successfully applied to
the study of free groups. Rational subsets of (free) groups can play a major
role in proving statements (a priori unrelated to the notion of rationality) by
induction. The chapter also includes related results for more general classes
of groups, such as virtually free groups or graph groups. |
Year | Venue | Keywords |
|---|---|---|
2010 | Clinical Orthopaedics and Related Research | automata theory,formal language,discrete mathematics,group theory,free group |
Field | DocType | Volume |
Stallings theorem about ends of groups,Discrete mathematics,Free product,Combinatorics,Classification of finite simple groups,Group theory,Group (mathematics),Bass–Serre theory,Free probability,Mathematics,Ping-pong lemma | Journal | abs/1012.1 |
Citations | PageRank | References |
2 | 0.40 | 6 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Laurent Bartholdi | 1 | 27 | 8.74 |
| Pedro V. Silva | 2 | 141 | 29.42 |