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Interconnections between the structure theory of set addition and rewritability in groups


Authors: Gregory A. Freiman and Boris M. Schein
Journal: Proc. Amer. Math. Soc. 113 (1991), 899-910
MSC: Primary 20F99; Secondary 20F05
DOI: https://doi.org/10.1090/S0002-9939-1991-1072338-3
MathSciNet review: 1072338
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Abstract: An approach to groups and semigroups stemming from the structure theory of set addition turns out to have much in common with the so-called permutation or rewritable properties. We explain these connections and show how these properties take their place in a wider class of interesting and naturally arising problems. As an example, we characterize some classes of groups and group elements.


References [Enhancements On Off] (What's this?)

  • [1] R. D. Blyth and D. J. S. Robinson, Recent progress on rewritability in groups, Group Theory (Proc. of the 1987 Singapore Conf.), de Gruyter, Berlin, 1988. MR 981835 (90b:20035)
  • [2] L. V. Brailovsky and G. A. Freiman, On two-element subsets in groups, Ann. New York Acad. Sci., vol. 373, 1981, New York Acad. Sci., New York, pp. 183-190. MR 719039 (84k:20003)
  • [3] -, On a product of finite subsets in a torsion-free group, J. Algebra 130 (1990), 462-476. MR 1051314 (91c:20052)
  • [4] L. V. Brailovsky, G. A. Freiman, and M. Herzog, Special elements in groups, Group Theory (Proc. 2nd Internat. Conf., Bressanone, Italy 1989), Suppl. Rend. Circ. Mat. Palermo, II. Ser. 23 (1990), 33-42. MR 1068347 (91g:20035)
  • [5] M. Curzio, P. Longobardi, and M. Maj, Su di un problema combinatorio in teoria dei gruppi, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 74 (1983), 136-142. MR 739397 (85k:20119)
  • [6] G. A. Freiman, Foundations of a structural theory of set addition, Kazan, 1966 (Russian); English transi.: Trans. Math. Monographs, Amer. Math. Soc., Providence, RI, 1973. MR 0360496 (50:12944)
  • [7] -, Groups and the inverse problems of the additive set theory, Number-Theoretic Investigations of the Markov Spectrum and the Structure Theory of Set Addition, Kalinin Univ., Moscow, 1973, pp. 175-183. (Russian)
  • [8] -, On two-and three-element subsets of groups, Aequationes Math. 22 (1981), 140-152. MR 645414 (83e:20029)
  • [9] -, What is the structure of $ K$ if $ K + K$ is small? Lecture Notes in Math., vol. 1240, Springer-Verlag, New York, 1987, pp. 109-134.
  • [10] G. A. Freiman and B. M. Schein, Group and semigroup theoretic considerations inspired by inverse problems of the additive number theory, Lecture Notes in Math., vol. 1320, Springer-Verlag, New York, 1988, pp. 121-140. MR 957761 (89j:20040)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1072338-3
Article copyright: © Copyright 1991 American Mathematical Society

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