Relationships between the Factors of the Central Series and the Nilpotent Residual in Some Infinite Groups

Abstract

We consider some natural relationships between the factors of the central series in groups. It was proved that if $G$ is a locally generalized radical group and $G/\zeta_k(G)$ has finite section $p$-rank $r$ (for some positive integer $k$), then $G$ includes a normal subgroup $L$ such that $G/L$ is nilpotent. Moreover, there exists a function $g$ such that $sr_p(L)\leq g(r)$.

Keywords

• finite section p-rank
• hypercenter
• nilpotent residual