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Finite p-groups with a minimal non-abelian subgroup of index p(Ⅱ) 被引量：10

Finite p-groups with a minimal non-abelian subgroup of index p(Ⅱ)
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摘要 We classify completely three-generator finite p-groups G such that Ф(G)≤Z(G)and|G′|≤p2.This paper is a part of the classification of finite p-groups with a minimal non-abelian subgroup of index p,and solve partly a problem proposed by Berkovich. We classify completely three-generator finite p-groups G such that Ф（G）≤Z（G）and｜G′｜≤p2.This paper is a part of the classification of finite p-groups with a minimal non-abelian subgroup of index p,and solve partly a problem proposed by Berkovich.
作者 AN LiJian LI LiLi QU HaiPeng ZHANG QinHai
机构地区 School of Mathematics and Computation Science School of Mathematics and Computation Science
出处 《Science China Mathematics》 SCIE 2014年第4期737-753,共17页 中国科学：数学（英文版）
基金 supported by National Natural Science Foundation of China (Grant No. 11371232) Natural Science Foundation of Shanxi Province (Grant Nos. 2012011001-3 and 2013011001-1)
关键词 minimal non-abelian p-groups At-groups congruent relation sub-congruent relation 有限p-群 非交换 子群 极小 发电机 基团
分类号 O152.1 [理学—基础数学] O151.21 [理学—基础数学]
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参考文献12

  • 1An L J, Hu R F, Zhang Q H. Finite p-groups with a minimal non-abelian subgroup of index p (Ⅳ). ArXiv:1310.5503.
  • 2Berkovich Y. Groups of Prime Power Order I. Berlin-New York: Walter de Gruyter, 2008.
  • 3Fang X G, An L J. A classification of finite metahamiltonian p-groups. ArXiv:1310.5509.
  • 4Hall M, Senior J K. The Groups of Order 2n (n≤ 6). New York: MacMillan, 1964.
  • 5Huppert B. Endliche Gruppen I. Berlin: Springer-Verlag, 1967.
  • 6Qu H P, Xu M Y, An L J. Finite p-groups with a minimal non-abelian subgroup of index p (Ⅲ). ArXiv:1310.5496.
  • 7Qu H P, Yang S S, Xu M Y, et al. Finite p-groups with a minimal non-abelian subgroup of index p (Ⅰ). J Algebra,2012, 358: 178-188.
  • 8Qu H P, Zhao L B, Gao J, et al. Finite p-groups with a minimal non-abelian subgroup of index p (V). J Algebra Appl, submitted.
  • 9Tuan H F. A theorem about p-groups with abelian subgroup of index p. Acad Sinica Science Record, 1950, 3: 17-23.
  • 10Xu M Y. An Introduction to Finite Groups (in Chinese). Beijing: Science Press, 1987.

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Science China Mathematics
2014年 第4期

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