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- Title
GROUP EXTENSIONS OVER INFINITE WORDS.
- Authors
DIEKERT, VOLKER; MYASNIKOV, ALEXEI
- Abstract
Non-Archimedean words have been introduced as a new type of infinite words which can be investigated through classical methods in combinatorics on words due to a length function. The length function, however, takes values in the additive group of polynomials ℤ[t] (and not, as traditionally, in ℕ), which yields various new properties. Non-Archimedean words allow to solve a number of interesting algorithmic problems in geometric and algorithmic group theory. There is also a connection to logic and the first-order theory in free groups (Tarski Problems). In the present paper we provide a general method to use infinite words over a discretely ordered abelian group as a tool to investigate certain group extensions for an arbitrary group G. The central object is a group (A, G) which is defined in terms of a non-terminating, but confluent rewriting system. The groupG as well as some natural HNN-extensions of G embed into (A, G) (and still "behave like" G), which makes it interesting to study its algorithmic properties. In order to show that every group G embeds into (A, G) we combine methods from combinatorics on words, string rewriting and group theory.
- Subjects
COMBINATION (Linguistics); REWRITING systems (Computer science); DISCRETE groups; FREE groups; POLYNOMIALS; EMBEDDING theorems
- Publication
International Journal of Foundations of Computer Science, 2012, Vol 23, Issue 5, p1001
- ISSN
0129-0541
- Publication type
Article
- DOI
10.1142/S0129054112400424