Syntactic and Rees indices of subsemigroups

Journal of Algebra

Volumn 205, Issue 2, 1998, Pages 435-450

  Ruskuc N ^a   Thomas, R M ^b  

^a UNIVERSITY OF ST ANDREWS   (United Kingdom)

^b UNIVERSITY OF LEICESTER   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001521246     PISSN: 00218693     EISSN: None     Source Type: Journal    
DOI: 10.1006/jabr.1997.7392     Document Type: Article

References (28)

1. S. I. Adyan, The unsolvability of certain algorithmic problems in the theory of groups, Trudy Moskov. Mat. Obshch. 6 (1957), 231-298. [In Russian]
2. C. M. Campbell, E. F. Robertson, N. Ruškuc, and R. M. Thomas, Reidemeister-Schreier type rewriting for semigroups, Semigroup Forum 51 (1995), 47-62.
3. C. M. Campbell, E. F. Robertson, N. Ruškuc, and R. M. Thomas, Rewriting a semigroup presentation, Internat. J. Algebra Comput. 5 (1995), 81-103.
4. C. M. Campbell, E. F. Robertson, N. Ruškuc, and R. M. Thomas, On subsemigroups of finitely presented semigroups, J. Algebra 180 (1996), 1-21.
5. C. M. Campbell, E. F. Robertson, N. Ruškuc, and R. M. Thomas, On subsemigroups and ideals in free products of semigroups, Internat. J. Algebra Comput. 6 (1996), 571-591.
6. C. M. Campbell, E. F. Robertson, N. Ruškuc, and R. M. Thomas, Presentations for subsemigroups - applications to ideals of semigroups, J. Pure Appl. Algebra 124 (1998), 47-64.
7. A. H. Clifford and G. B. Preston, "The Algebraic Theory of Semigroups, Vol. 2," Amer. Math. Soc., Providence, 1967.
8. P. Dubreil, "Contribution à la théorie des demi-groupes," Mém. Acad. Sci. Inst., France, 1941.
9. J. M. Howie, "Fundamentals of Semigroup Theory," Clarendon, Oxford, 1995.
10. A. Jura, Coset enumeration in a finitely presented semigroup, Canad. Math. Bull. 21 (1978), 37-46.
11. A. Jura, Determining ideals of a given finite index in a finitely presented semigroup, Demonstratio Math. 11 (1978), 813-827.
12. A. Jura, Some remarks on non-existence of an algorithm for finding all ideals of a given finite index in a finitely presented semigroup, Demonstratio Math. 13 (1980), 573-578.
13. G. Lallement, "Semigroups and Combinatorial Applications," Wiley, New York, 1979.
14. S. A. Linton, Generalisations of the Todd-Coxeter algorithm, in "Computational Algebra and Number Theory" (W. Bosma and A. van der Poorten, Eds.), pp. 29-51, Kluwer Academic, Dordrecht, 1995.
15. W. Magnus, A. Karrass, and D. Solitar, "Combinatorial Group Theory," Interscience, New York, 1966.
16. A. Markov, The impossibility of certain algorithms in the theory of associative systems, Dokl. Akad. Nauk SSSR 77 (1951), 19-20. [In Russian]
17. A. Markov, The impossibility of algorithms for the recognition of certain properties of associative systems, Dokl. Akad. Nauk SSSR 77 (1951), 953-956. [In Russian]
18. J. Neubüser, An elementary introduction to coset table methods in computational group theory, in "Groups - St. Andrews, 1981" (C. M. Campbell and E. F. Robertson, Eds.), pp. 1-45, Cambridge Univ. Press, Cambridge, 1982.
19. B. H. Neumann, Some remarks on semigroup presentations, Canad. J. Math. 19 (1967), 1018-1026.
20. M. O. Rabin, Recursive unsolvability of group theoretic problems, Ann. Math. 67 (1958), 172-194.
21. K. Reidemeister, Knoten und Gruppen, Abh. Math. Sem. Hamburg Univ. 5 (1926), 7-23.
22. E. F. Robertson and Y. Ünlü, On semigroup presentations, Proc. Edinburgh Math. Soc. 36 (1993), 55-68.
23. N. Ruškuc, "Semigroup Presentations," Ph.D. Thesis, University of St Andrews, 1995.
24. N. Ruškuc, On large subsemigroups and finiteness conditions of semigroups, Proc. London Math. Soc. 76 (1998), 383-405.
25. O. Schreier, Die Untergruppen der freien Gruppen, Abh. Math. Sem. Hamburg Univ. 5 (1927), 161-183.
26. C. C. Sims, "Computation with Finitely Presented Groups," Cambridge Univ. Press, Cambridge, 1994.
27. J. A. Todd and H. S. M. Coxeter, A practical method for enumerating the cosets of a finite abstract group, Proc. Edinburgh Math. Soc. 5 (1936), 26-34.
28. T. G. Walker, "Semigroup Enumeration - Computer Implementation and Applications," Ph.D. Thesis, University of St Andrews, 1992.