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- W4308613670 abstract "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 $mathrm{PSL}(2,q)$ is given." @default.
- W4308613670 created "2022-11-13" @default.
- W4308613670 creator A5036540493 @default.
- W4308613670 date "2022-11-06" @default.
- W4308613670 modified "2023-09-27" @default.
- W4308613670 title "Characterizing subgroup perfect codes by 2-subgroups" @default.
- W4308613670 doi "https://doi.org/10.48550/arxiv.2211.03120" @default.
- W4308613670 hasPublicationYear "2022" @default.
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