Thompson subgroup

《Abstract Algebra》 · 第 139 页 · Section 4.4「Automorphisms」，Exercise 20 的定义段

For any finite group $P$ let $d(P)$ be the minimum number of generators of $P$ (so, for example, $d(P)=1$ if and only if $P$ is a nontrivial cyclic group and $d(Q_8)=2$). Let $m(P)$ be the maximum of the integers $d(A)$ as $A$ runs over all abelian subgroups of $P$ (so, for example, $m(Q_8)=1$ and $m(D_8)=2$). Define $J(P)=\langle A\mid A\text{ is an abelian subgroup of }P\text{ with }d(A)=m(P)\rangle$. ($J(P)$ is called the Thompson subgroup of $P$.)