Abstract
The notion of conjugacy in groups can be extended in two ways to monoids. We keep on calling conjugacy the first version (two elements x and y are conjugate if xz=zy holds for some z), while we call transposition the second one (two elements x and y are transposed conjugate if x=uv and y=vu holds for some u,v). Using the characterization of elements in free inverse monoids due to Munn, we show that restricted to non idempotents, the relation of conjugacy is the transitive closure of the relation of transposition. Furthermore, we show that conjugacy between two elements of a free inverse monoid can be tested in linear time.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
Berstel J., “Transductions and Context-Free languages”, Teubner Verlag, 1979.
Booth K., S., Lexicographically least circular substrings, Inform. Proc. Let., 4, (1980), pp. 240–242
Duval J.-P., Factorizing words over an ordered alphabet, Journal of Algorithms, 4, (1983), pp. 363–381
Duboc C., On some equations in free partially commutative monoids, Theofet. Comput.Sci., 46, 1986, pp. 159–174
Howie J.M., “An Introduction to Semigroup Theory”, Academic Press, (1976)
Lallement G., “Semigroups and Combinatorial Applications”, J. Wiley, New York, (1979).
Lentin A. & M.P. Schützenberger, A combinatorial problem in the theory of free monoids, Proc. University of North Carolina, (1967), 128–144
Lyndon R. & Schützenberger M.-P., The equation aM=bNcP in a free group, Mich. Math. J., 9, (1962), 289–298
Meakin J., Automata and the word problem, Proc. of the 16-th LITP Spring School on Theoretical Computer Science, Lecture Notes in Computer Science, 386, pp. 89–103
Magnus W., Karrass A. and Solitar D., Combinatorial Group Theory, 2nd ed., Dover, New York, (1976)
Munn W.D., Free Inverse Semigroups, Proc. London Math. Soc., 3, 1974, pp. 385–404
Narendram P. and Otto F., The problems of cyclic equality and conjugacy for finite complete rewriting systems, 47, (1986), pp. 27–38
Narendram P., Otto F. and Winklmann, The Uniform Conjugacy Problems for Finite Church-Rosser Thue Systems Is NP-Complete. 63, (1984). pp. 58–66
Osipova V.A., On the conjugacy problem in semigroups, Proc. Steklov Inst. Math., 133, (1973), pp. 169–182
Otto F., Conjugacy in monoids with a special Church-Rosser presentation is Decidable, Semigroup Forum, 29, (1984), pp. 223–240
Scheiblich H.E., Free Inverse Semigroups, Semigroup Forum, 4, 1972, pp. 351–359
Scheiblich H.E., Free Inverse Semigroups, Proc. Amer. Math. Soc., 8, 1973, PP. 1–7
Stephen J.B., The word problem for inverse monoids and related questions, to appear
Zhang L., Conjugacy in special Monoids, to appear in J. of Algebra
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Choffrut, C. (1993). Conjugacy in free inverse monoids. In: Abdulrab, H., Pécuchet, JP. (eds) Word Equations and Related Topics. IWWERT 1991. Lecture Notes in Computer Science, vol 677. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56730-5_28
Download citation
DOI: https://doi.org/10.1007/3-540-56730-5_28
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-56730-1
Online ISBN: 978-3-540-47636-8
eBook Packages: Springer Book Archive