2025/07/21 by chen, Huye, Li, Binbin, Li, Jingjian +1
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2507.15206
A subset C of the vertex set of a graph Γ is called a perfect code in Γ if every vertex of Γ is at distance no more than 1 to exactly one vertex of C. A subgroup H of a group G is called a subgroup perfect code of G if H is a perfect code in some Cayley graph of G. Recently, Zhang reveals that the study of subgroup perfect codes of finite groups naturally reduces to the case of p-groups, especially 2-groups. Based on the combined works of Berkovich, Janko and Zhang, every p-group is an At-group. In this work, we establish a complete classification of subgroup perfect codes of At-groups for t ∈\0, 1\. Moreover, subgroup perfect codes of finite groups with abelian Sylow 2-subgroups are also characterized.