On Factor Groups of some Groups

Abstract: Let for a prime $p$, $\mathfrak{X}$ (respectively $\mathfrak{Y}$) be the class of all $p$-biprimitively finite (respectively periodic $p$-conjugatively biprimitively finite) groups and $G\in \mathfrak{X}$ (respectively $G\in \mathfrak{Y}$), $V$ be a periodic subgroup of $G$ having an ascending series of normal in $G$ subgroups such that each its factor is an almost layer-finite group or a locally graded group of finite special rank, or a $WF$-group with $min-q$ on all primes $q$. We prove that $G/V \in \mathfrak{X}$ (respectively $G/V\in \mathfrak{Y}$). Also some interesting and useful preliminary results are obtained.