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

Document Type: Research Paper

Author

School of Mathematical and Computer Sciences‎, ‎University of Limpopo (Turfloop)‎, ‎P‎. ‎Bag X1106‎, ‎Sovenga 0727‎, ‎South Africa.

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..

Keywords

Main Subjects

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### History

• Receive Date: 12 May 2016
• Revise Date: 22 October 2016
• Accept Date: 22 October 2016