대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제52권2호
  • /
  • Pages.367-376
  • /
  • 2015
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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FINITE p-GROUPS WHOSE NON-CENTRAL CYCLIC SUBGROUPS HAVE CYCLIC QUOTIENT GROUPS IN THEIR CENTRALIZERS

  • Zhang, Lihua (Beijing University of Posts and Telecommunications) ;
  • Wang, Jiao (Department of Mathematics Shanxi Normal University) ;
  • Qu, Haipeng (Department of Mathematics Shanxi Normal University)
  • 투고 : 2013.04.09
  • 발행 : 2015.03.31
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초록

In this paper, we classified finite p-groups G such that $$C_G(x)/<x>$$ is cyclic for all non-central elements $x{\in}G$. This solved a problem proposed By Y. Berkovoch.

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과제정보

연구 과제 주관 기관 : NSFC

참고문헌

  1. Y. Berkovich, Groups of Prime Power Order, Volume 1, Walter de Gruyter, Berlin, 2008.
  2. Y. Berkovich and Z. Janko, Structure of finite p-groups with given subgroups, Contemp. Math. 402, 13-93, Amer. Math. Soc., Providence, RI, 2006. https://doi.org/10.1090/conm/402/07570
  3. N. Blackburn, Generalizations of certain elementary theorems on p-groups, Proc. London Math. Soc. (3) 11 (1961), 1-22.
  4. B. Huppert, Endliche Gruppen I, Springer-Verlag, 1967.
  5. K. Ishikawa, Finite p-groups up to isoclinism, which have only two conjugacy lengths, J. Algebra 220 (1999), no. 1, 333-354. https://doi.org/10.1006/jabr.1999.7907
  6. X. H. Li and J. Q. Zhang, Finite p-groups and centralizers of non-central elements, Comm. Algebra 41 (2013), no. 9, 3267-3276. https://doi.org/10.1080/00927872.2012.682676
  7. M. Y. Xu, L. J. An, and Q. H. Zhang, Finite p-groups all of whose non-abelian proper subgroups are generated by two elements, J. Algebra 319 (2008), no. 9, 3603-3620. https://doi.org/10.1016/j.jalgebra.2008.01.045