Ons-Length of Groups

• Autorzy: Olga Macedońska , Aleksandra Potyka
• Języki publikacji: EN

Abstrakty

EN

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)

Słowa kluczowe

EN

Mathematics; Mathematic calculations; Mathematical functions; Isomorphism

PL

Matematyka; Obliczenia matematyczne; Funkcje matematyczne; Izomorfizm

• Czasopismo: Annales Mathematicae Silesianae
• Rocznik: 2008
• Tom: 22
• Strony: 59--67

Twórcy

autor

Olga Macedońska

• Silesian University of Technology, Poland

autor

Aleksandra Potyka

• Silesian University of Technology, Poland

Bibliografia

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