The ranks of the classes of $A_{10}$

Abstract

‎Let $G $ be a finite group and $X$ be a conjugacy class of $G.$ The‎ ‎rank of $X$ in $G,$ denoted by $rank(G{:}X),$ is defined to‎ ‎be the minimal number of elements of $X$ generating $G.$ In this‎ ‎paper we establish the ranks of all the conjugacy classes of‎ ‎elements for simple alternating group $A_{10}$ using the structure‎ ‎constants method and other results established in‎ ‎[A.B.M‎. ‎Basheer and J‎. ‎Moori‎, ‎On the ranks of the alternating group $A_{n}$‎, ‎Bull‎. ‎Malays‎. ‎Math‎. ‎Sci‎. ‎Soc..