A subset $B$ of a group $G$ is called basis if each element $g\in G$ can be written as $g=ab$ for some elements $a,b\in B$. The smallest cardinality $|B|$ $B\subseteq the size and denoted by $r[G]$. We prove that finite has $r[G]>\sqrt{|G|}$. If Abelian, then $r[G]\ge \sqrt{2|G|-|G|/|G_2|}$, where $G_2=\{g\in G:g^{-1} = g\}$. Also we calculate sizes all Abelian groups order $\le 60$ non-Abel...