${P_5}$群的Chermak-Delgado格

Abstract

简称Chermak-Delgado格为CD格,${\rm{CD}}\left( G \right)$代表群G的CD格.若$\left| G; \right.\left| { = {p^n},} \right.\left| {G:Z\left( G \right)\left| { =; {p^i},G \in } \right.CD\left( G \right)}; \right.$,则称$G$是${P_i}$群.研究了$\left| {G:Z\left( G \right)\left| { = {p^5}}; \right.} \right.$群$G$的CD格,转化为研究${P_5}$群的CD格.确定了${P_5}$群的CD格的Hasse图.

In this paper,${\rm{CD}}\left( G \right)$ means the Chermak-Delgado; lattice of a group G.If $\left| G \right.\left| { = {p^n},}; \right.\left| {G:Z\left( G \right)\left| { = {p^i},G \in }; \right.CD\left( G \right)} \right.$,then we assert that G is a; ${P_i}$-group.In this paper,we give all Hasse graphs of ${\rm{CD}}\left(; G \right)$,where G denotes ${P_5}$-groups.