RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Subscription Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Algebra Logika: Year: Volume: Issue: Page: Find

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

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.

Full text: PDF file (372 kB)
References: PDF file   HTML file

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

Bibliographic databases:

UDC: 512.542
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
\Bibitem{Aha12} \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 \mathnet{http://mi.mathnet.ru/al559} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3088137} \zmath{https://zbmath.org/?q=an:06189468} \transl \jour Algebra and Logic \yr 2013 \vol 51 \issue 6 \pages 451--478 \crossref{https://doi.org/10.1007/s10469-013-9206-0} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000316014000001} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84880703023} 

• http://mi.mathnet.ru/eng/al559
• http://mi.mathnet.ru/eng/al/v51/i6/p683

 SHARE:

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
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
3. I. B. Gorshkov, “Towards Thompson's conjecture for alternating and symmetric groups”, J. Group Theory, 19:2 (2016), 331–336
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
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
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
•  Number of views: This page: 218 Full text: 32 References: 37 First page: 13