A new investgation on Steinberg groups $^3{}D_4(q)$
Abstract
In this paper, we prove that simple groups $^3{}D_4(q)$, where $q^4-q^2+1$ is a prime number can be uniquely determined by the order of group and the second largest element order.
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References
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\bibitem{art:Chen2} G. Y. Chen, L. G. He, J. H. Xu.
A new characterization of sporadic simple groups,
\emph{Italian journal of pure and mathematics},
{\bf 30}, (2013), 373-392.
\bibitem{art:Chen3} G. Y. Chen, L. G. He.
A new characterization of $L_2(q)$ where $q=p^n<125$
\emph{Italian journal of pure and mathematics},
{\bf }38,(2011), 125-134.
\bibitem{art:Chen4} G. Y. Chen, L. G. He.
A new characterization o simple $K_4$ -group with type $L_2(p)$
\emph{Advanced in mathematics(china)},
{\bf43 }, no.5, (2014), 667-670.
\bibitem{art:Ebrahimzadeh} B. Ebrahimzadeh, A. Iranmanesh, A. Tehranian, H. Parvizi Mosaed.
A Characterization of the suzuki groups by order and the largest elements order
\emph{J. Sci. Islamic. Rep. Iran},
{\bf27 }, no. 4, (2016), 353-355.
\bibitem{art:Ebrahimzadeh1} B. Ebrahimzadeh, R. Mohammadyari,
A new characterization of projective special unitary groups $PSU_3(3^n)$,
\emph{Discussiones Mathematicae General Algebra and Applications},
{\bf39 }, (2019), 35-41.
\bibitem{art:Ebrahimzadeh2} B. Ebrahimzadeh, M. Y. Sadeghi, A. Iranmanesh, A. Tehranian,
A new characterization of symplectics groups $PSP(8,q)$,
\emph{Analele Stiintifice ale Universitatii Alexandru Ioan Cuza din Iasi},
{\bf 66}, no.1,(2020), p93-99, 7p.
\bibitem{art:Ebrahimzadeh3} B. Ebrahimzadeh, R. Mohammadyari, M. Y. Sadeghi,
A new characterization of simple groups $C_4(q)$ by its order and the largest order of elements,
\emph{Acta et Commentationes Universitatis Tartuensis de Mathematica},
{\bf 23}, no. 2, (2019), 283-290.
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Recognition of the simple groups $^2{}D_8(2^n)^2)$ by its order and the largest order of elements,
\emph{Analele universitatii de vest Timisoara seria Mathematica Informatica LvII},
{\bf 2} (2019),1-8.
\bibitem{art:Ebrahimzadeh5} B. Ebrahimzadeh, A. R. Khalili Asboei,
A characterization of symplectic groups related to Fermat primes,
\emph{Commentationes Mathematicae Universitatis Carolinae},
{\bf 62}, no.1, (2021), 33-40.
\bibitem{art:Ebrahimzadeh6} B. Ebrahimzadeh,
A new characterization of simple groups $^2{}D_n (3)$,
\emph{Transactions Issue Mathematics, Azerbaijan National Academy of Sciences},
{\bf 41}, no. 4, (2021), 57-62.
\bibitem{art:Ebrahimzadeh7}B. Ebrahimzadeh, B. Azizi,
A characterization of projective special linear groups $ PSL (5, 2)$ and $PSL (4, 5)$,
\emph{Annals of the Alexandru Ioan Cuza University-Mathematics},
{\bf 68}, no. 1, (2022), p.133-140. 8p.
\bibitem{art:Ebrahimzadeh8} B. Ebrahimzadeh,
On the Suzuki Groups,
\emph{Asian Journal of Pure and Applied Mathematics},
{\bf 3}, no.1, (2021), 67-71.
\bibitem{book:Gor} D. Gorenstein.
Finite groups, Harper and Row, New York,
(1980).
\bibitem{book:He} L. G. He, G. Y. Chen.
A new characterization of $L_3(q)$ $(q\le 8)$ and $U_3(q)$ $(q\le 11)$,
\emph{J. Southwest Univ. (Natur.Sci.)},
{\bf27 }, no.33,(2011), 81-87.
\bibitem{art:Kantor} W. M. Kantor, A. Seress.
Large element orders and the characteristic of Lie-type simple groups,
\emph{J. Algebra},
{\bf 322},(2009), 802-832.
\bibitem{art:Kondrat'ev} A. S. Kondrat'ev,
Prime graph components of finite simple groups,
\emph{Mathematics of the USSR-Sbornik},
{\bf 67}(1)(1990), 235-247 .
\bibitem{book:Li} J. Li, W. J. Shi, D. Yu.
A characterization of some $PGL(2,q)$ by maximum element orders,
\emph{Bull.Korean Math.Soc},
{\bf 52}, no. 6, (2015), 2025-2034.
\bibitem{art:Shi5} Shi, W.J.-
A characterization of $U_3(2^n)$ by their element orders
\emph{ J Southwest-China Normal Univ},
{\bf 25}(4)(2000), 353-360
\bibitem{art:Will} J. S. Williams.
Prime graph components of finite groups,
\emph{J. Algebra},
{\bf 69}, no. 2,(1981), 487-513.
\bibitem{art:Dapeng}D. Yu, J. Li, G. Chen, L. Zhang and W.J. Shi,
A new characterization of simple $K_5$-groups of type $L_3(p)$
\emph{Bull. Iranian Math. Soc},
{\bf 45}(2019), 771-781.
\bibitem{art:Zav} A. V. Zavarnitsine.
Recognition of the simple groups $L_3(q)$ by element orders,
\emph{J. Group Theory},
{\bf 7}, no.1, (2004), 81-97.
Published
2025-10-30
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