Bases in finite groups of small order - Banakh, T.O.; Gavrylkiv, V.M. (Carpathian Mathematical Publications, 2021)
A subset B of a group G is called a basis of G if each element gG can be written as g=ab for some elements a,bB. The smallest cardinality |B| of a basis BG 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|/|G_2|, where G_2={gG:g^-1 = g}. Also we calculate the basis sizes of all Abelian groups of order 60 and all non-Abelian groups of order 40.