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Rationality of Verbal Subsets in Solvable Groups

Authors
  • Roman’kov, V. A.
Type
Published Article
Journal
Algebra and Logic
Publisher
Springer US
Publication Date
Mar 01, 2018
Volume
57
Issue
1
Pages
39–48
Identifiers
DOI: 10.1007/s10469-018-9477-6
Source
Springer Nature
Keywords
License
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Abstract

A verbal subset of a group G is a set w[G] of all values of a group word w in this group. We consider the question whether verbal subsets of solvable groups are rational in the sense of formal language theory. It is proved that every verbal subset w[N] of a finitely generated nilpotent group N with respect to a word w with positive exponent is rational. Also we point out examples of verbal subsets of finitely generated metabelian groups that are not rational.

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