References
C.J. Ash, Finite semigroups with commuting idempotents,J. Austral. Math. Soc. (Series A) 43, 1987.
J.C. Birget, S.W. Margolis and J. Rhodes, Finite semigroups whose idempotents commute or form a subsemigroup,in Semigroups and Their Applications, edited by S.M. Goberstein and P.M. Higgins, Reidel, Dordrecht, 1987, pp. 25–35.
J.C. Birget, S.W. Margolis and J. Rhodes, Finite semigroups whose idempotents form a semilattice or a band. To appear.
S. Eilenberg,Automata, Languages and Machines, Academic Press, New York, vol. A, 1974; Vol B, 1976.
M. Hall Jr., A topology for free groups and related groups,Ann. of Maths,52, (1950), 127–139.
J. Karnofsky and J. Rhodes, Decidability of complexity one-half for finite semigroups,Semigroup Forum 24 (1982) 55–66
G. Lallement,Semigroups and Combinatorial Applications, Wiley, New York, 1979.
S.W. Margolis and J.E. Pin, Varieties of finite monoids and topology for the free monoid. InProceedings of the Marquette Semigroup Conference, 1984, pp. 113–130.
S.W. Margolis and J.E. Pin, Product of group languages, FCT Conference, Lecture Notes in Computer Science 199 (1985) 285–299.
S.W. Margolis and J.E. Pin, Inverse semigroups and varieties of finite semigroups,Journal of Algebra 110 (1987) 306–323.
J.E. Pin, Finite group topology andp-adic topology for free monoids.12th ICALP, Lecture Notes in Computer Science 199, Springer, Berlin, 1985, pp. 285–299.
J.E. Pin,Varieties of formal languages, North Oxford Academic, London and Plenum, New-York, 1986.
J.E. Pin, On the languages recognized by finite reversible automata,14th ICALP, Lecture Notes in Computer Science 267 Springer, Berlin, 1987, pp. 237–249.
J.E. Pin, A topological approach to a conjecture of Rhodes. To appear in the Bulletin of the Australian Mathematical Society.
J.E. Pin, Topologies for the free monoid. Submitted.
Ch. Reutenauer, Une topologie du monoïde libre,Semigroup Forum 18 (1979) 33–49.
Ch. Reutenauer, Sur mon article “Une topologie du monoïde libre”,Semigroup Forum,22 (1981) 93–95.
J. Rhodes, New techniques in global semigroup theory, inSemigroups and Their Applications, edited by S.M. Goberstein and P.M. Higgins, Reidel, Dordrecht, 1987, pp. 169–181.
J. Rhodes and B. Tilson, Improved lower bounds for the complexity of finite semigroups,Journal of Pure and Applied Algebra 2 (1972), 13–71.
B. Tilson,Chapter XI and XII of reference [4]
B. Tilson, Type II redux, inSemigroups and Their Applications, edited by S.M. Goberstein and P.M. Higgins, Reidel, Dordrecht, 1987, pp., 201–205.
Author information
Authors and Affiliations
Additional information
Communicated by Boris M. Schein
This work was supported by the PRC Mathématiques et Informatique.
Rights and permissions
About this article
Cite this article
Pin, J.E. On a conjecture of Rhodes. Semigroup Forum 39, 1–15 (1989). https://doi.org/10.1007/BF02573280
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02573280