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Let $G$ be a group and let $p$ be a fixed prime. For each positive integer $n$, the $n$-th term of the Jennings-Lazard-Zassenhaus series of the group $G$ is defined by the rule \begin{eqnarray*} D_{n} …

Let $G$ be a fixed group. for each property $P$ of groups, $G$ is said to be residually-$P$ if for each $1\neq g\in G$ there exists $N\unlhd G$ such that $g\notin N$ and $G/N$ has the property $P$. If …

I know that every finite Engel group is a nilpotent group. Then, if $G$ is a residually finite Engel group, every finite quotient group of $G$ is a nilpotent group. Is necesseraly true that $G$ is a n …