 Fitting subgroup

The largest nilpotent normal subgroup of a finite group $G$. If $O_p(G)$ denotes its p-core, distinct p-cores commute, and $F(G)={\prod }_p{O}_p(G)$. Every normal nilpotent group has Sylow subgroups which are characteristic subgroups, so it is contained in this product.

In group theory, a **fitting subgroup** is a concept related to the structure of finite groups. Specifically, the Fitting subgroup of a group \( G \), denoted as \( F(G) \), is defined as the largest nilpotent normal subgroup of \( G \). ### Key Points about Fitting Subgroup: 1. **Nilpotent Group**: A group is nilpotent if its upper central series terminates in the whole group after finitely many steps.