Turkish Journal of Mathematics
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].
DOI
10.55730/1300-0098.3120
Keywords
Finite groups, nonsolvable groups, conjugacy class, index
First Page
746
Last Page
752
Recommended Citation
ROBATI, S. M, & BALAMAN, R. H (2022). Non-solvable groups all of whose indices are odd-square-free. Turkish Journal of Mathematics 46 (3): 746-752. https://doi.org/10.55730/1300-0098.3120
