Rationality of Verbal Subsets in Solvable Groups
- 作者: Roman’kov V.A.1
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隶属关系:
- Dostoevskii Omsk State University
- 期: 卷 57, 编号 1 (2018)
- 页面: 39-48
- 栏目: Article
- URL: https://journal-vniispk.ru/0002-5232/article/view/234072
- DOI: https://doi.org/10.1007/s10469-018-9477-6
- ID: 234072
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详细
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.
作者简介
V. Roman’kov
Dostoevskii Omsk State University
编辑信件的主要联系方式.
Email: romankov48@mail.ru
俄罗斯联邦, pr. Mira 55-A, Omsk, 644077
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