Bases in finite groups of small order

Keywords:
finite group, Abelian group, basis, basis size, basis characteristic
Published online:
2021-06-20
Abstract
A subset of a group is called a basis of if each element can be written as for some elements . The smallest cardinality of a basis is called the basis size of and is denoted by . We prove that each finite group has . If is Abelian, then , where . Also we calculate the basis sizes of all Abelian groups of order and all non-Abelian groups of order .
How to Cite
(1)
Banakh, T.; Gavrylkiv, V. Bases in Finite Groups of Small Order. Carpathian Math. Publ. 2021, 13, 149-159.