Products of groups and class sizes of $\pi$-elements

M. J. Felipe, A. Martínez-Pastor, V. M. Ortiz-Sotomayor

We provide structural criteria for some finite factorised groups $G=AB$ when the conjugacy class sizes in $G$ of certain $\pi$-elements in $A\cup B$ are either $\pi$-numbers or ${\pi }^{\prime }$-…