Journal of applied mathematics & informatics

  • 제7권1호
  • /
  • Pages.115-124
  • /
  • 2000
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  • 2734-1194(pISSN)
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  • 2234-8417(eISSN)
한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
권호 표지

COUNTING THE CINTRALIZERS OF SOME FINITE GROUPS

  • Ashrafi, Ali Reza (Institute for Studids in Theoretical Physics and Mathematics, Department of Mathematics, Faculty of Science, University of Kashan)
  • 발행 : 2000.01.01

⟨ 이전 논문 다음 논문 ⟩

초록

For a finite group G, #Cent(G) denotes the number of cen-tralizers of its clements. A group G is called n-centralizer if #Cent( G) = n. and primitive n-centralizer if #Cent(G) = #Cent(${\frac}{G}{Z(G)$) = n. In this paper we compute the number of distinct centralizers of some finite groups and investigate the structure of finite groups with Qxactly SLX distinct centralizers. We prove that if G is a 6-centralizer group then ${\frac}{G}{Z(G)$${\cong}D_8$,$A_4$, $Z_2{\times}Z_2{\times}Z_2$ or $Z_2{\times}Z_2{\times}Z_2{\times}Z_2$.

키워드

참고문헌

  1. Southeast Asian Bulletin of Mathematics v.2 On the n-sum groups, n = 6, 7 A.R. Ashrafi
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