Let G be a finite group and N(G)be its norm.Then N(G)is a characteristic subgroup of G which normalizes every subgroup of G.In this paper,we will study the structure of G under one of the following conditions:1)norm q...Let G be a finite group and N(G)be its norm.Then N(G)is a characteristic subgroup of G which normalizes every subgroup of G.In this paper,we will study the structure of G under one of the following conditions:1)norm quotient group G/N(G)is cyclic;2)all Sylow subgroups of G/N(G)are cyclic and in particular if the order of G/N(G)is a square-free number.展开更多
Let G be a finite group,H be a nonnormal subgroup of G.The subgroup H^(G)=<H^(g)|g∈G>is called the normal closure of H in G.Let Δ(G)={|HG||H 5 G}.G is called aΔk-group if |Δ(G)|=k.AΔ_(k-p)-group means G is ...Let G be a finite group,H be a nonnormal subgroup of G.The subgroup H^(G)=<H^(g)|g∈G>is called the normal closure of H in G.Let Δ(G)={|HG||H 5 G}.G is called aΔk-group if |Δ(G)|=k.AΔ_(k-p)-group means G is both a finite p-group and a Δk-group.In this paper,Δ_(2-p)-groups G with d(G)=2 are classified by central extension,where p is an odd prime.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11661023)the Service Industry Development Guide of Guizhou Province(Grant No.Qian Fa Gai Fu Wu[2018]1181)。
文摘Let G be a finite group and N(G)be its norm.Then N(G)is a characteristic subgroup of G which normalizes every subgroup of G.In this paper,we will study the structure of G under one of the following conditions:1)norm quotient group G/N(G)is cyclic;2)all Sylow subgroups of G/N(G)are cyclic and in particular if the order of G/N(G)is a square-free number.
文摘Let G be a finite group,H be a nonnormal subgroup of G.The subgroup H^(G)=<H^(g)|g∈G>is called the normal closure of H in G.Let Δ(G)={|HG||H 5 G}.G is called aΔk-group if |Δ(G)|=k.AΔ_(k-p)-group means G is both a finite p-group and a Δk-group.In this paper,Δ_(2-p)-groups G with d(G)=2 are classified by central extension,where p is an odd prime.
