2022/02/20 by Gang Chen, Chen, Gang, Ren Qing +1
Engineering · Mathematics · #20B05 #20D10 #20D25 #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2202.09765
openalex publication_date 2022/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let N be a normal subgroup of a finite group G. For a faithful N-set Δ, applying the university embedding theorem one can construct a faithful G-set Ω. In this short note, it is proved that if the 2-closure of N in Ω is equal to N, then the 2-closure of N in Δ is also equal to N; in addition, it is proved that any abelian normal subgroup of a finite totally 2-closed group is cyclic; finally, it is proved that if a finite nilpotent group is a direct of two nilpotent subgroups where the two factors have coprime orders and both of them are totally 2-closed then G is totally 2-closed. As corollaries, several well-known results on finite totally 2-closed groups are reproved in more simple ways.