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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Elements of finite order for finite monadic Church-Rosser Thue systems
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by Friedrich Otto PDF
Trans. Amer. Math. Soc. 291 (1985), 629-637 Request permission

Abstract:

A Thue system $T$ over $\Sigma$ is said to allow nontrivial elements of finite order, if there exist a word $u \in {\Sigma ^ \ast }$ and integers $n \ge 0$ and $k \ge 1$ such that $u \nleftrightarrow _T^ \ast \lambda$ and ${u^{n + k}} \leftrightarrow _T^ \ast {u^n}$. Here the following decision problem is shown to be decidable: Instance. A finite, monadic, Church-Rosser Thue system $T$ over $\Sigma$. Question. Does $T$ allow nontrivial elements of finite order? By a result of Muller and Schupp this implies in particular that given a finite monadic Church-Rosser Thue system $T$ it is decidable whether the monoid presented by $T$ is a free group or not.
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Additional Information
  • © Copyright 1985 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 291 (1985), 629-637
  • MSC: Primary 03D03; Secondary 03D40, 20F10, 68Q45
  • DOI: https://doi.org/10.1090/S0002-9947-1985-0800255-1
  • MathSciNet review: 800255