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Algebra Logika, 2012, Volume 51, Number 6, Pages 683–721 (Mi al559)  

This article is cited in 6 scientific papers (total in 6 papers)

Thompson's conjecture for some finite simple groups with connected prime graph

N. Ahanjideh

Dep. Math., Shahrekord Univ., Shahrekord, Iran

Abstract: Let $n$ be an even number and either $q=8$ or $q>9$. We prove a conjecture of Thompson (Problem 12.38 in the Kourovka Notebook) for an infinite class of finite simple groups of Lie type. More precisely, if $S\in\{C_n(q),B_n(q)\}$, then every finite group $G$ for which $Z(G)=1$ and $N(G)=N(S)$ will be isomorphic to $S$. Note that $N(G)=\{n\colon G$ has a conjugacy class of size $n\}$. The main consequence of this result is showing the validity of $AAM$'s conjecture (Problem 16.1 in the Kourovka Notebook) for the groups under study.

Keywords: simple group, minimal normal subgroup, conjugacy class, centralizer.

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English version:
Algebra and Logic, 2013, 51:6, 451–478

Bibliographic databases:

UDC: 512.542
Received: 18.11.2011
Revised: 25.08.2012

Citation: N. Ahanjideh, “Thompson's conjecture for some finite simple groups with connected prime graph”, Algebra Logika, 51:6 (2012), 683–721; Algebra and Logic, 51:6 (2013), 451–478

Citation in format AMSBIB
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\by N.~Ahanjideh
\paper Thompson's conjecture for some finite simple groups with connected prime graph
\jour Algebra Logika
\yr 2012
\vol 51
\issue 6
\pages 683--721
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\jour Algebra and Logic
\yr 2013
\vol 51
\issue 6
\pages 451--478
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Sh. Liu, Y. Yang, “On Thompson's conjecture for alternating groups $A_{p+3}$”, Sci. World J., 2014, 752598  crossref  isi  scopus
    2. Chen Ya., Chen G., “Characterization of Pgl(2, P) By Its Order and One Conjugacy Class Size”, Proc. Indian Acad. Sci.-Math. Sci., 125:4 (2015), 501–506  crossref  mathscinet  zmath  isi
    3. I. B. Gorshkov, “Towards Thompson's conjecture for alternating and symmetric groups”, J. Group Theory, 19:2 (2016), 331–336  crossref  mathscinet  zmath  isi  elib  scopus
    4. N. Ahanjideh, “Thompson's conjecture for finite simple groups of Lie type $B_n$ and $C_n$”, J. Group Theory, 19:4 (2016), 713–733  crossref  mathscinet  zmath  isi  scopus
    5. N. Ahanjideh, “Thompson's conjecture on conjugacy class sizes for the simple group $PSU_n(q)$”, Int. J. Algebr. Comput., 27:6 (2017), 769–792  crossref  mathscinet  zmath  isi  scopus
    6. A. Kh. Asboei, M. R. Darafsheh, R. Mohammadyari, “The influence of order and conjugacy class length on the structure of finite groups”, Hokkaido Math. J., 47:1 (2018), 25–32  crossref  mathscinet  zmath  isi
  • Алгебра и логика Algebra and Logic
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