p-constrained group
= p-constrained group
Put $\overline G=G/O_{p'}(G)$ using the <p-prime core of a finite group>. A finite <group> is p-constrained if $C_{\overline G}(O_p(\overline G))\le O_p(\overline G)$. If $O_{p'}(G)=1$, the <p-core of a finite group> has its centralizer contained in itself. Then <block idempotents centralize a normal p-subgroup> places every block idempotent in $kO_p(G)$, a <local ring>, so $kG$ has only the <principal block>.