Grushko-like theorems for a class of finitely presented semigroups

Author:
Ann Yasuhara

Journal:
Proc. Amer. Math. Soc. **42** (1974), 359-364

MSC:
Primary 20M05

MathSciNet review:
0335665

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Abstract: An analogue of Grushko's theorem and the unsolvability of the isomorphism problem hold for semigroups in the class of all finitely presented semigroups that have a presentation in which there is no defining relation of the form ; this class is not recursive but is recursively enumerable.

**[C&P]**A. H. Clifford and G. B. Preston,*The algebraic theory of semigroups. Vol. II*, Mathematical Surveys, No. 7, American Mathematical Society, Providence, R.I., 1967. MR**0218472****[D]**Martin Davis,*Computability and unsolvability*, McGraw-Hill Series in Information Processing and Computers, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1958. MR**0124208****[K]**A. G. Kuroš,*Theory of groups*, GITTL, Moscow, 1953; English transl., Vol II, Chelsea, New York, 1960. MR**15**, 501;**22**#727.**[M]**A. A. Markov,*Theory of algorithms*, Translated by Jacques J. Schorr-Kon and PST Staff, Published for The National Science Foundation, Washington, D.C. and The Department of Commerce by The Israel Program for Scientific Translations, Jerusal, 1961. MR**0132690****[MK&S]**Wilhelm Magnus, Abraham Karrass, and Donald Solitar,*Combinatorial group theory: Presentations of groups in terms of generators and relations*, Interscience Publishers [John Wiley & Sons, Inc.], New York-London-Sydney, 1966. MR**0207802****[Mo]**A. Mostowski,*Review of A. A. Markov's impossibility of algorithms for recognizing some properties of associative systems*, J. Symbolic Logic**17**(1952), p. 151.**[R]**Michael O. Rabin,*Recursive unsolvability of group theoretic problems*, Ann. of Math. (2)**67**(1958), 172–194. MR**0110743****[Y1]**Ann Yasuhara,*Recursive function theory and logic*, Academic Press, New York-London, 1971. Computer Science and Applied Mathematics. MR**0313027****[Y2]**-,*Some non-recursive classes of semi-groups with solvable word problem*, Z. Math. Logik Grundlagen Math. (to appear).

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1974-0335665-0

Keywords:
Finitely presented semigroup,
free product,
rank,
decision problem

Article copyright:
© Copyright 1974
American Mathematical Society