Warianty tytułu
Języki publikacji
Abstrakty
Let G be a group and S be a subsemigroup in G, generating G as a group. Every element in G is a product of elements from S∪S-1. An equality G = S - 1 S···S - 1 S allows to define an S-length l (G) of the group G. The note concerns the problem posed by J. Krempa on possible values of l (G). We show that for collapsing groups, supramenable groups and groups of a subexponential growth l (G) ≤ 2. The S - length of a relatively free group can be equal to 1 or 2 or infinity, but it can not be equal to 3. The problem concerning other values is open. (original abstract)
Twórcy
autor
- Silesian University of Technology, Poland
autor
- Silesian University of Technology, Poland
Bibliografia
- Clifford A.H., Preston G.B., The Algebraic Theory of Semigroups, Vol. I, American Mathematical Society, R.I., 1964.
- Erschler A., Not residually finite groups of intermediate growth, commensurability and non-geometricity, J. Algebra272(2004), 154-172.
- Grigorchuk R.I., On the Milnor problem of group growth (Russian), Dokl. Akad. Nauk SSSR 271 (1) (1983), 30-33. English translation: Soviet Math. Dokl. 28 (1) (1983), 23-26.
- Gromov M., Groups of polynomial growth and expanding maps, Inst. Hautes Études Sci. Publ. Math. 53 (1981), 53-78.
- Ivanov S.V., Storozhev A.M., Non-Hopfian relatively free groups, Geom. Dedicata 114 (2005), 209-228.
- Neumann H., Varieties of Groups, Springer-Verlag, Berlin-Heidelberg-New York, 1967.
- Semple J.F., Shalev A., Combinatorial conditions in residually finite groups I, J. Algebra 157 (1993), 43-50.
- Wagon S., The Banach-Tarski Paradox, Cambridge University Press, 1985.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
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