Some special coprime actions and their consequence

Gülin Ercan, İsmail Ş. Güloğlu, M. Yasir Kızmaz, Danila O. Revin

Published 2021-05-22Version 1

Let a group $A$ act on the group $G$ coprimely. Suppose that the order of the fixed point subgroup $C_G(A)$ is not divisible by an arbitrary but fixed prime $p$. In the present paper we determine bounds for the $p$-length of the group $G$ in terms of the order of $A$, and investigate how some $A$-invariant $p$-subgroups are embedded in $G$ under various additional assumptions.