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Algebra i logika, 2002, Volume 41, Number 1, Pages 70–82 (Mi al172)  
This article is cited in 5 scientific papers (total in 5 papers)

The Number of Isomorphism Classes of Finite Groups with Given Element Orders

H. Denga, M. S. Lucido, W. Shi

a Southwest China Normal University
Full-text PDF (1199 kB) Citations (5)
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Abstract: Let $G$ be a finite group and $\pi_e(G)$ the set of element orders of $G$. Denote by $h(\pi_e(G))$ the number of isomorphism classes of finite groups $H$ satisfying $\pi_e(H)=\pi_e(G)$. We prove that if $G$ has at least three prime graph components, then $h(\pi_e(G))\in\{1, \infty\}$.
Keywords: finite group, set of element orders of a group, prime graph.
Received: 08.08.2000
Revised: 26.04.2000
English version:
Algebra and Logic, 2002, Volume 41, Issue 1, Pages 39–46
DOI: https://doi.org/10.1023/A:1014658001689
Bibliographic databases:
UDC: 519.542
Language: Russian
Citation: H. Deng, M. S. Lucido, W. Shi, “The Number of Isomorphism Classes of Finite Groups with Given Element Orders”, Algebra Logika, 41:1 (2002), 70–82; Algebra and Logic, 41:1 (2002), 39–46
Citation in format AMSBIB
\Bibitem{DenLucShi02}
\by H.~Deng, M.~S.~Lucido, W.~Shi
\paper The Number of Isomorphism Classes of Finite Groups with Given Element Orders
\jour Algebra Logika
\yr 2002
\vol 41
\issue 1
\pages 70--82
\mathnet{http://mi.mathnet.ru/al172}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1924598}
\zmath{https://zbmath.org/?q=an:1016.20014}
\transl
\jour Algebra and Logic
\yr 2002
\vol 41
\issue 1
\pages 39--46
\crossref{https://doi.org/10.1023/A:1014658001689}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-22744455520}
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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