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Finite 2-generator equilibrated p-groups
【摘要】 <正>Following Blackburn, Deaconescu and Mann, a group G is called an equilibrated group if for any subgroups H,K of G with HK = KH, either H≤NG(K) or K≤NG(H). Continuing their work and based on the classification of metacyclic p-groups given by Newman and Xu, we give a complete classification of 2-generator equilibrated p-groups in this note.
【Abstract】 Following Blackburn, Deaconescu and Mann, a group G is called an equilibrated group if for any subgroups H,K of G with HK = KH, either H≤NG(K) or K≤NG(H). Continuing their work and based on the classification of metacyclic p-groups given by Newman and Xu, we give a complete classification of 2-generator equilibrated p-groups in this note.
【关键词】 equilibrated group；
metacyclic group；
finite p-group；
minimal non-abelian group；
【Key words】 equilibrated group； metacyclic group； finite p-group； minimal non-abelian group；
【Key words】 equilibrated group； metacyclic group； finite p-group； minimal non-abelian group；
【基金】 This work was partially supported by the National Natural Science Foundation of China (Grant No. 10671114);the Natural Science Foundation of Shanxi Province (Grant No. 20051007)
- 【文献出处】 Science in China(Series A:Mathematics) ,中国科学(A辑:数学)(英文版) , 编辑部邮箱 ,2007年06期
- 【分类号】O152.1
- 【被引频次】1
- 【下载频次】18