可解群的中心化子的阶的一个性质

A Prperty of the orders of centralizers o Solvable groups

设ZO(G)={|CG(x)||x∈G\Z(G)},pz(G)=|{p|p|k,p为素数，k∈ZO(G)}|．σ(k)=|{p|p|k,p为素数}|σz(G)=max{σ(k)|k∈ZO(G)}．本文证明了：若G是可解群，则Pz(G)≤Zσz(G)．

let ZO(G)={|CG(x)||x∈G\Z(G)},pz(G)=|{p|p|k, p is prime } |,σ(k)=|{p|p|k,p is prime}|,σz(G)=max{σ(k)|k ∈ ZO(G)}. In thispaper, we prove that if G is a solvable group, then Pz(G)≤Zσz(G).