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http://dx.doi.org/10.4134/JKMS.2008.45.1.137

ON NON-ISOMORPHIC GROUPS WITH THE SAME SET OF ORDER COMPONENTS  

Darafsheh, Mohammad Reza (Department of Mathematics, Statistics and Computer Science Faculty of Science, University of Tehran)
Publication Information
Journal of the Korean Mathematical Society / v.45, no.1, 2008 , pp. 137-150 More about this Journal
Abstract
In this paper we will prove that the simple groups $B_p(3)\;and\;G_p(3)$, p an odd prime number, are 2-recognizable by the set of their order components. More precisely we will prove that if G is a finite group and OC(G) denotes the set of order components of G, then OC(G) = $OC(B_p(3))$ if and only if $G{\cong}B_p(3)\;or\;C_p(3)$.
Keywords
prime graph; order component; linear group;
Citations & Related Records

Times Cited By Web Of Science : 3  (Related Records In Web of Science)
Times Cited By SCOPUS : 3
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1 A. Khosravi and B. Khosravi, r-recognizability of $B_{n}(q)$ and $C_{n}(q)$ where $n =2^{m}\;{\geq}\;4$, J. Pure Appl. Algebra 199 (2005), no. 1-3, 149-165   DOI   ScienceOn
2 J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, and R. A. Wilson, Atlas of Finite Groups, Clarendon Press, Oxford, 1985
3 P. Crescenzo, A Diophantine equation which arises in the theory of finite groups, Advances in Math. 17 (1975), no. 1, 25-29   DOI
4 J. S. Williams, Prime graph components of finite groups, J. Algebra 69 (1981), no. 2, 487-513   DOI
5 K. Zsigmondy, Zur Theorie der Potenzreste, Monatsh. Math. Phys. 3 (1892), no. 1, 265-284   DOI
6 G. Y. Chen, On Thompson's conjecture, J. Algebra 185 (1996), no. 1, 184-193   DOI   ScienceOn
7 S. H. Alavi and A. Daneshkhah, A new characterization of alternating and symmetric groups, J. Appl. Math. Comput. 17 (2005), no. 1-2, 245-258   DOI
8 G. Y. Chen, A new characterization of sporadic simple groups, Algebra Colloq. 3 (1996), no. 1, 49-58
9 G. Y. Chen, A new characterization of $PSL_{2}(q)$, Southeast Asian Bull. Math. 22 (1998), no. 3, 257-263
10 G. Y. Chen, On Frobenius and 2-Frobenius groups, J. Southwest China Normal Univ. 20 (1995), no. 5, 485-487
11 G. Y. Chen and H. Shi, $^2D_n(3)9{\leq}n=2^m$ + 1 not a prime) can be characterized by its order components, J. Appl. Math. Comput. 19 (2005), no. 1-2, 353-362   DOI
12 A. Iranmanesh, S. H. Alavi, and B. Khosravi, A characterization of PSL(3, q) where q is an odd prime power, J. Pure Appl. Algebra 170 (2002), no. 2-3, 243-254   DOI   ScienceOn
13 A. Iranmanesh, S. H. Alavi, and B. Khosravi, A characterization of PSL(3,q) for $q =2^{m}$, Acta Math. Sin. (Engl. Ser.) 18 (2002), no. 3, 463-472   DOI
14 Behrooz Khosravi, Behnam Khosravi, and Bahman Khosravi, The number of isomorphism classes of finite groups with the set of order components of $C_{4}(q)$, Appl. Algebra Engrg. Comm. Comput. 15 (2005), no. 5, 349-359   DOI
15 A. Iranmanesh, B. Khosravi, and S. H. Alavi, A characterization of $PSU_{3}$(q) for q > 5, Southeast Asian Bull. Math. 26 (2002), no. 1, 33-44   DOI   ScienceOn
16 A. Khosravi and B. Khosravi, A new characterization of PSL(p,q), Comm. Algebra 32 (2004), no. 6, 2325-2339   DOI   ScienceOn
17 A. Khosravi and B. Khosravi, A new characterization of some alternating and symmetric groups, Int. J. Math. Math. Sci. (2003), no. 45, 2863-2872
18 A. S. Kondratev, On prime graph components of finite simple groups, Mat. Sb. 180 (1989), no. 6, 787-797
19 H. Shi and G. Y. Chen, $^{2}D_{p+1}$(2)(5${\leq}p{\neq}2^{m}-1$) can be characterized by its order components, Kumamoto J. Math. 18 (2005), 1-8