A new characterization of groups $\mathbf{ B_4 (q )}$
DOI:
https://doi.org/10.5269/bspm.63575Resumen
One of an important problems in finite groups theory is, characterizable of groups by specific property. In this paper, we prove that groups $B_4 (q)$, where $3< q$ be prime number and $ \frac{q^4+1}{2}$ is a prime number, can be uniquely determined by the largest elements order and the order of group.
Referencias
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16. A. Khosravi, and B. Khosravi, A new characterization of some alternating and symmetric groups (II) Houston J. Math, 30(4)(2004), 465-478.
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19. A. V. Zavarnitsine, Recognition of the simple groups L3(q) by element orders, J. Group Theory. 7(1)(2004), 81-97.
2. G. Y. Chen, L. G. He and J. H. Xu, A new characterization of sporadic simple groups, Italian journal of pure and mathematics. 30(2013), 373-392.
3. G. Y. Chen, L. G. He, A new characterization of L2(q) where q = pn < 125, Italian journal of pure and mathematics. 38(2011),125-134 .
4. G. Y. Chen, L. G. He, A new characterization o simple K4 -group with type L2(p) Advanced in mathematics(china). (2012)doi: 10.11845/sxjz.165b .
5. Ebrahimzadeh, B., Iranmanesh, A., Tehranian, A and Parvizi Mosaed, H., A characterization of the suzuki groups by order and the largest elements order, Journal of sciences, islamic republic of iran . 27(4),(2016), 353-355.
6. Ebrahimzadeh, B., Mohammadyari, R., A new characterization of projective special unitary groupsPSU3(3n), Discussiones Mathematicae: General Algebra and Applications. 39 (1)(2019),35-41.
7. Ebrahimzadeh, B., A new characterization of simple groups 2Dn(3), Transactions Issue Mathematics, Azerbaijan National Academy of Sciences. 41 (4)(2019),57-62.
8. Ebrahimzadeh, B., Azizi, B., A characterization of projective special linear groups PSL(5, 2) and PSL(4, 5), Annals of the Alexandru Ioan Cuza University-Mathematics. 68 (1)(2022),133-140.
9. Ebrahimzadeh, B., Sadeghi, M. Y., Iranmanesh, A and Tehranian, A., A new characterization of symplectics groups PSP(8, q), Annals of the Alexandru Ioan Cuza University-Mathematics. 66 (1)(2020), 93-99.
10. Ebrahimzadeh, B., Mohammadyari, R and Sadeghi, M. Y., A new characterization of the simple groups C4(q), by its order and the largest order of elements, Acta et Commentationes Universitatis Tartuensis de Mathematica . 23 (2)(2019), 283-290.
11. D. Gorenstein, Finite groups, Harper and Row, New York,(1980).
12. L. G. He, G.Y. Chen, A new characterization of L3(q) (q 8) and U3(q) (q 11), J. Southwest Univ. (Natur.Sci.), 27 (33)(2011), 81-87.
13. G. Higman, Finite groups in which every element has prime power order, J. London. Math. Soc), 32 (1957), 335-342.
14. W. M. Kantor and A, Seress, Large element orders and the characteristic of Lie-type simple groups, J. Algebra. 322 (2009), 802-832 .
15. A. S. Kondrat’ev, Prime graph components of finite simple groups, Mathematics of the USSR-Sbornik, 67(1)(1990), 235-247.
16. A. Khosravi, and B. Khosravi, A new characterization of some alternating and symmetric groups (II) Houston J. Math, 30(4)(2004), 465-478.
17. J. Li, W. J. Shi, and D. Yu, A characterization of some PGL(2, q) by maximum element orders, Bull. Korean Math. Soc. 322(2009), 802-832.
18. J. S. Williams, Prime graph components of finite groups, J. Algebra. 69(2)(1981), 487-513.
19. A. V. Zavarnitsine, Recognition of the simple groups L3(q) by element orders, J. Group Theory. 7(1)(2004), 81-97.
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2024-05-20
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