A perfect code in a graph \(\Gamma \) is a subset C of \(V(\Gamma )\) such that no two vertices in C are adjacent and every vertex in \(V(\Gamma ){\setminus } C\) is adjacent to exactly one vertex in C. Let G be a finite group and C a subset of G. Then C is said to be a perfect code of G if there exists a Cayley graph of G admiting C as a perfect code. It is proved that a subgroup H of G is a perfect code of G if and only if a Sylow 2-subgroup of H is a perfect code of G. This result provides a way to simplify the study of subgroup perfect codes of general groups to the study of subgroup perfect codes of 2-groups. As an application, a criterion for determining subgroup perfect codes of projective special linear groups \(\textrm{PSL}(2,q)\) is given.

图\(\Gamma \)中的完美编码是\(V(\Gamma )\)的子集C，使得C中没有两个顶点相邻并且\(V(\Gamma ){\setminus } C\)恰好与C中的一个顶点相邻。令G为有限群，C为G的子集。如果存在 G 的 Cayley 图承认C是一个完美代码，则称C是G 的一个完美代码。证明了G的一个子群H是G的一个完美码当且仅当H的 Sylow 2-子群是G的完美代码。该结果提供了一种将一般群的子群完全码研究简化为2-群子群完全码研究的途径。作为一个应用，给出了确定射影特殊线性群\(\textrm{PSL}(2,q)\)子群完美码的判据。