| Autor: |
T. O., Banakh, V. M., Gavrylkiv |
| Předmět: |
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| Zdroj: |
Carpathian Mathematical Publications / Karpats'kì Matematičnì Publìkacìï; 2021, Vol. 13 Issue 1, p149-159, 11p |
| Abstrakt: |
A subset B of a group G is called a basis of G if each element g ∈ G can be written as g = ab for some elements a, b ∈ B. The smallest cardinality |B| of a basis B ⊆ G is called the basis size of G and is denoted by r [G]. We prove that each finite group G has r [G] > √ |G|. If G is Abelian, then r [G] ≥ √ 2 |G|−|G| / |G2|, where G2 = {g∈G:g−1 =g} . Also we calculate the basis sizes of all Abelian groups of order ≤ 60 and all non-Abelian groups of order ≤ 40. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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