Literature cited
R. I. Grigorchuk, “On the growth of finite automata under iterations,” Abstracts of the Reports of the All-Union Conference on Applied Logic [in Russian], Novosibirsk (1985).
M. Gromov, “Groups of polynomial growth and expanding maps,” Publ. Math. IHES,53, No. 1, 53–73 (1981).
H. Bass, “The degree of polynomial growth of finitely generated nilpotent groups,” Proc. London Math. Soc.,25, No. 4, 603–614 (1972).
V. I. Trofimov, “Growth functions of algebraic systems,” Candidate's Thesis, Physico-mathematical Sciences, Sverdlovsk (1982).
A. I. Mal'tsev, “Nilpotent Semigroups,” Uch. Zap. Ivanovsk. Pedagog. Inst.,4, 107–111 (1953).
A. H. Clifford and G. B. Preston, The Algebraic Theory of Semigroups, Vol. I, Am. Math. Soc., Providence (1961).
Y. M. Rosenblatt, “Invariant measures and growth conditions,” Trans. Am. Math. Soc.,193, No. 1, 33–53 (1974).
F. P. Greenleaf, Invariant Means of Topological Groups and Their Applications, Van Nostrand Reinhold, New York (1969).
A. H. Frey, Studies in Amenable Semigroups; dissertation, Univ. of Washington, Seattle, Wash. (1960).
S. Wagon, The Banach-Tarski Paradox, Encyclopedia of Mathematics and Its Applications, Vol. 24, Cambridge Univ. Press (1985).
E. Hewitt and K. A. Ross, Abstract Harmonic Analysis, Vol. I, Springer-Verlag, Berlin-New York (1963).
L. Dries and A. Wilkie, “Gromov's theorem on groups of polynomial growth and elementary logic,” J. Algebra,89, No. 2, 349–374 (1984).
R. I. Grigorchuk, “Degrees of growth of finitely generated groups and theory of invariant means,” Izv. Akad. Nauk SSSR, Ser. Mat.,48, No. 5, 939–985 (1984).
R. I. Grigorchuk, “On the degrees of growth of p-groups and torsion-free groups,” Mat. Sb.,126, No. 2, 194–214 (1985).
M. I. Kargapolov and Yu. I. Merzlyakov, Fundamentals of Group Theory [in Russian], Nauka, Moscow (1982).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 43, No. 3, pp. 305–319, March, 1988.
Rights and permissions
About this article
Cite this article
Grigorchuk, R.I. Cancellative semigroups of power growth. Mathematical Notes of the Academy of Sciences of the USSR 43, 175–183 (1988). https://doi.org/10.1007/BF01138837
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01138837