Non-solvable groups all of whose indices are odd-square-free

Authors: SAJJAD MAHMOOD ROBATI, ROGHAYEH HAFEZIEH BALAMAN

Abstract: Given a finite group $G$ and $x\in G$, the class size of $x$ in $G$ is called odd-square-free if it is not divisible by the square of any odd prime number. In this paper, we show that if $G$ is a nonsolvable finite group, all of whose class sizes are odd-square-free, then we have some control on the structure of $G$, which is an answer to the dual of the question mentioned by Huppert in [5].

Keywords: Finite groups, nonsolvable groups, conjugacy class, index

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