Let G be a finite group. Roughly speaking, a subgroup A of G is called a local partial covering subgroup if $A^G=AB$ for a suitable maximal G-invariant subgroup B of $A^G$. Our main result is as follows: Let $p^d$ be a prime power with $p\le p^d\le \sqrt{|G{|}_p}$, assume that all subgroups of $p^d$, and all cyclic subgroups of order 4 when $p^d=2$ and a Sylow 2-subgroup of G is nonabelian, of G are local partial covering subgroups. Then $G/O_{p^{\prime }p}(G)$ is p-supersolvable; furthermore if G is not p-supersolvable, then $O_{p^{\prime }p}(G)/\mathrm{\Phi }$ is a homogeneous ${\mathcal{F}}_p[G]$-module where $\mathrm{\Phi }/O_{p^{\prime }}(G)=\mathrm{\Phi }(G/O_{p^{\prime }}(G))$, and each irreducible constituent has dimension dividing $d-{\log }_p|\mathrm{\Phi }{|}_p$.

令G为有限群。粗略地说，子组甲的ģ称为本地部分覆盖亚组是否${\mathrm{一种}}^G=\mathrm{一种}乙$一个合适的最大ģ -invariant亚乙的${\mathrm{一种}}^G$。我们的主要结果如下：$p^d$ 与...成为主要力量 $p\le p^d\le \sqrt{|G{|}_p}$，假设的所有子组 $p^d$，以及4阶时的所有循环子组 $p^d=2$G的Sylow 2子群是nonabelian，G的是局部局部覆盖子群。然后$G/{Ø}_{p^{\prime }p}（G）$是p-超可解的; 此外，如果G不是p-超可解的，则${Ø}_{p^{\prime }p}（G）/\mathrm{\Phi }$ 是同质的 ${\mathcal{F}}_p[G]$-模块在哪里 $\mathrm{\Phi }/{Ø}_{p^{\prime }}（G）=\mathrm{\Phi }（G/{Ø}_{p^{\prime }}（G））$，并且每个不可约成分都有维度划分 $d-{\mathrm{日志}}_p|\mathrm{\Phi }{|}_p$。