A group is a pair $(G, \cdot)$ consisting of a set G and a binary operation ( $\cdot$ ) on it such that the following properties are satisfied: 1) $\forall a,b,c \in G: a \cdot (b \cdot c) =(a \cdot b) \cdot c$ (associativity); 2) $\exists e \in G\ \forall a \in G: a \cdot e =e \cdot a = a$ (the existance of the identily element); 3) $\forall a \in G\ \exists a^{-1} \in G : a \cdot a^{-1}= a^{-1} \cdot a = e$ (the existence of the inverse). A group $G$ is called finite group if there are finite number of elements in $G$. The number of elements in a finite group is called the order of a group and is denoted by $|G|$.