Free Burnside Semigroups
Alair Pereira do Lago; Imre Simon
RAIRO - Theoretical Informatics and Applications (2010)
- Volume: 35, Issue: 6, page 579-595
- ISSN: 0988-3754
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topAlair Pereira do Lago, and Simon, Imre. "Free Burnside Semigroups." RAIRO - Theoretical Informatics and Applications 35.6 (2010): 579-595. <http://eudml.org/doc/221966>.
@article{AlairPereiradoLago2010,
abstract = {
This paper surveys the area of Free Burnside Semigroups. The theory of
these semigroups, as is the case for groups, is far from being completely
known. For semigroups, the most impressive results were obtained in the
last 10 years. In this paper we give priority to the mathematical treatment of the problem
and do not stress too much neither motivation nor the historical aspects.
No proofs are presented in this paper, but we tried to give as many examples
as was possible.
},
author = {Alair Pereira do Lago, Simon, Imre},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {free Burnside semigroups; relatively free semigroups; varieties of semigroups},
language = {eng},
month = {3},
number = {6},
pages = {579-595},
publisher = {EDP Sciences},
title = {Free Burnside Semigroups},
url = {http://eudml.org/doc/221966},
volume = {35},
year = {2010},
}
TY - JOUR
AU - Alair Pereira do Lago
AU - Simon, Imre
TI - Free Burnside Semigroups
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/3//
PB - EDP Sciences
VL - 35
IS - 6
SP - 579
EP - 595
AB -
This paper surveys the area of Free Burnside Semigroups. The theory of
these semigroups, as is the case for groups, is far from being completely
known. For semigroups, the most impressive results were obtained in the
last 10 years. In this paper we give priority to the mathematical treatment of the problem
and do not stress too much neither motivation nor the historical aspects.
No proofs are presented in this paper, but we tried to give as many examples
as was possible.
LA - eng
KW - free Burnside semigroups; relatively free semigroups; varieties of semigroups
UR - http://eudml.org/doc/221966
ER -
References
top- S.I. Adian, The Burnside problem and identities in groups. Springer-Verlag, Berlin-New York, Ergebnisse der Mathematik und ihrer Grenzgebiete 95 [Results in Mathematics and Related Areas] (1979). Translated from the Russian by John Lennox and James Wiegold.
- S.I. Adyan, The Burnside problem and identities in groups. Izdat. ``Nauka'', Moscow (1975).
- J. Brzozowski, Open problems about regular languages, edited by R.V. Book. Academic Press, New York, Formal Language Theory, Perspectives and Open Problems (1980) 23-47.
- J. Brzozowski, K. Culík and A. Gabrielian, Classification of non-counting events. J. Comput. System Sci.5 (1971) 41-53.
- J.A. Brzozowski and I. Simon, Characterizations of locally testable events. Discrete Math.4 (1973) 243-271.
- W. Burnside, On an unsettled question in the theory of discontinuous groups. Quart. J. Math.33 (1902) 230-238.
- A. de Luca and S. Varricchio, On non-counting regular classes, edited by M.S. Paterson, Automata, Languages and Programming. Springer-Verlag, Berlin, Lecture Notes in Comput. Sci. 443 (1990) 74-87.
- A. de Luca and S. Varricchio, On non-counting regular classes. Theoret. Comput. Sci.100 (1992) 67-104.
- A.P. do Lago, Local groups in free groupoids satisfying certain monoid identities (to appear).
- A.P. do Lago, Sobre os semigrupos de Burnsidexn = xn+m, Master's Thesis. Instituto de Matemática e Estatística da Universidade de S ao Paulo (1991).
- A.P. do Lago, On the Burnside semigroups xn = xn+m, in LATIN'92, edited by I. Simon. Springer-Verlag, Berlin, Lecture Notes in Comput. Sci. 583 (1992) 329-343.
- A.P. do Lago, On the Burnside semigroups xn=xn+m. Int. J. Algebra Comput.6 (1996) 179-227.
- A.P. do Lago, Grupos Maximais em Semigrupos de Burnside Livres, Ph.D. Thesis. Universidade de S ao Paulo (1998). Electronic version at<http://www.ime.usp.br/ alair/Burnside>
- A.P. do Lago, Maximal groups in free Burnside semigroups, in LATIN'98, edited by C.L. Lucchesi and A.V. Moura. Springer-Verlag, Berlin, Lecture Notes in Comput. Sci. 1380 (1998) 70-81.
- S. Eilenberg, Automata, languages, and machines, Vol. B. Academic Press [Harcourt Brace Jovanovich Publishers], New York (1976). With two chapters (``Depth decomposition theorem'' and ``Complexity of semigroups and morphisms'') by B. Tilson, Pures Appl. Math. 59.
- J.A. Green and D. Rees, On semigroups in which xr = x. Proc. Cambridge. Philos. Soc.48 (1952) 35-40.
- V.S. Guba, The word problem for the relatively free semigroup satisfying tm = tm+n with m ≥ 3. Int. J. Algebra Comput.2 (1993) 335-348.
- V.S. Guba, The word problem for the relatively free semigroup satisfying tm = tm+n with m ≥ 4 or m=3, n=1. Int. J. Algebra Comput.2 (1993) 125-140.
- M. Hall, Solution of the Burnside problem for exponent six. Illinois J. Math.2 (1958) 764-786.
- G. Huet and D.C. Oppen, Equations and rewrite rules: A survey, edited by R.V. Book. Academic Press, New York, Formal Language Theory, Perspectives and Open Problems (1980) 349-405.
- S.V. Ivanov, The free Burnside groups of sufficiently large exponents. Int. J. Algebra Comput. 4 (1994) ii+308.
- J. Kadourek and L. Polák, On free semigroups satisfying xr ≃ x. Simon Stevin64 (1990) 3-19.
- J.W. Klop, Term rewriting systems: From Church-Rosser to Knuth-Bendix and beyond, edited by M.S. Paterson, Automata, Languages and Programming. Springer-Verlag, Berlin, Lecture Notes in Comput. Sci. 443 (1990) 350-369.
- G. Lallement, Semigroups and Combinatorial Applications. John Wiley & Sons, New York (1979).
- F.W. Levi and B.L. van der Waerden, Über eine besondere Klasse von Gruppen. Abh. Math. Sem. Hamburg9 (1933) 154-158.
- I.G. Lysënok, Infinity of Burnside groups of period 2k for k ≥ 13. Uspekhi Mat. Nauk47 (1992) 201-202.
- S. MacLane, Categories for the working mathematician. Springer-Verlag, New York, Grad. Texts in Math. 5 (1971).
- J. McCammond, The solution to the word problem for the relatively free semigroups satisfying ta = ta+b with a ≥ 6. Int. J. Algebra Comput.1 (1991) 1-32.
- D. McLean, Idempotent semigroups. Amer. Math. Monthly61 (1954) 110-113.
- P.S. Novikov and S.I. Adjan, Infinite periodic groups. I. Izv. Akad. Nauk SSSR Ser. Mat. 32 212-244.
- P.S. Novikov and S.I. Adjan, Infinite periodic groups. II. Izv. Akad. Nauk SSSR Ser. Mat.32 (1968) 251-524.
- A.Y. Ol'shanski, Geometry of defining relations in groups. Kluwer Academic Publishers Group, Dordrecht (1991). Translated from the 1989 Russian original by Yu.A. Bakhturin.
- I. Sanov, Solution of Burnside's problem for exponent 4. Leningrad. Gos. Univ. Uchen. Zap. Ser. Mat.10 (1940) 166-170 (Russian).
- I. Simon, Notes on non-counting languages of order 2. Manuscript (1970).
- H. Straubing, Finite automata, formal logic, and circuit complexity. Birkhäuser Boston Inc., Boston, MA (1994).
- A. Thue, Über die gegenseitige Lage gleicher Teile gewisser Zeichenreihen. Norske Vid. Selsk. Skr. I Mat. Nat. Kl.1 (1912) 1-67.
- B. Tilson, Categories as algebra: An essential ingredient in the theory of monoids. J. Pure Appl. Algebra48 (1987) 83-198.
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