Chinese Quarterly Journal of Mathematics ›› 2006, Vol. 21 ›› Issue (4): 497-502.

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A Generalization of Cuccia's Theorem 

  


  1. College of Mathematics and Information Science Guangxi University,College of Mathematics and Information Science,Guangxi University,,Nanning 530004,China School of Science,Xi’an Polytechnic University,Xi’an 710048,China,Nanning 530004,China
  • Received:2005-03-28 Online:2006-12-30 Published:2023-11-17
  • About author:XU Ying-wu(1965-),male,native of Xi'an,Shaanxi,a lecturer of Xi'an Polytechnic University, engages in the theory of finite group;LI Shi-rong(1940-),male,native of Shaodong,Hunan,a professor of Guangxi University,engages in the theory of finite group.
  • Supported by:
     Supported by the Natural Science Foundation of Guangxi Autonomous Region(0249001)；

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Abstract: For a finite group G,let S(G)be the set of minimal subgroups of odd order of G which are complemented in G.It is proved that if every minimal subgroup X of odd order of G which does not belong to S(G),CG(X)is either subnormal or abnormal in G.Then G solvable.

Key words: the centralizer of a minimal subgroup, subnormal subgroups, abnormal sub-
group, solvable group

CLC Number: 

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