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A Characterization of the Smallest Suzuki 2-Group

A Characterization of the Smallest Suzuki 2-Group
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摘要 Let G be a finite nonabelian group which has no abelian maximal subgroups and satisfies that any two non-commutative elements generate a maximal subgroup. Then G is isomorphic to the smallest Suzuki 2-group of order 64. Let G be a finite nonabelian group which has no abelian maximal subgroups and satisfies that any two non-commutative elements generate a maximal subgroup. Then G is isomorphic to the smallest Suzuki 2-group of order 64.
作者 Qin Hai ZHANG
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2008年第12期2011-2014,共4页 数学学报(英文版)
基金 NSFC (No.10671114) NSF of Shanxi Province (No.20051007) the Returned Overseas(student) Fund of Shanxi province (No.[2007]13-56)
关键词 metacyclic groups minimal nonabelian groups Suzuki 2-groups metacyclic groups, minimal nonabelian groups, Suzuki 2-groups
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参考文献6

  • 1Higman, G.: Suzuki 2-groups. Illinois J. Math. 7, 79-96 (1963)
  • 2Huppert, B.: Endliche Gruppen Ⅰ, Springer-Verlag, New York, 1967
  • 3Tuan, H. F.: A theorem about p-groups with abelian subgroup of index p. Acad. Siniea Science Record, 3, 17-23 (1950)
  • 4Redei, L.: Das schiefe Product in der Gruppeatheorie. Comment. Math. Helvet., 20, 225 267 (1947)
  • 5Chen, Z. M.: Inner- and Outer-∑-Groups and Minimal Non-∑-Groups (Chinese), Southwest Teachers University Press, Chongqing, China, 1988
  • 6Blackburn, N.: Generalizations of certain elementary theorems on p-groups. Proc. London Math. Soc., 11(3), 1-22 (1961)

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