Recognition of the Simple Groups 2D8((2n)2)

Behnam Ebrahimzadeh

doi:10.2478/awutm-2019-0014

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Recognition of the Simple Groups 2D8((2n)2)

Annals of West University of Timisoara - Mathematics and Computer Science

Volume 57 (2019): Issue 2 (December 2019)

By: Behnam Ebrahimzadeh

Open Access

|Dec 2020

Abstract

One of the important problems in finite groups theory is group characterization by specific property. Properties, such as element orders, set of elements with the same order, the largest element order, etc. In this paper, we prove that the simple groups ²D₈((2ⁿ)²)where, 2⁸ⁿ+ 1 is a prime number are uniquely determined by its order and the largest elements order.

References

[1] G. Y. Chen, On the structure of Frobenius groups and 2-Frobenius groups, J. Southwest China Normal University, 20 (5), (1995), 485-487
Search in Google Scholar Back to article
[2] G. Y. Chen,L.G.He, andJ.H.Xu, A new characterization of sporadic simple groups, Italian Journal of Pure and Applied Mathematics, 30, (2013), 373-392
Search in Google Scholar Back to article
[3] G. Y. Chen and L. G. He, A new characterization of L₂(q)where q = pⁿ< 125, Italian Journal of Pure and Applied Mathematics, 38, (2011), 125-134
Search in Google Scholar Back to article
[4] G. Y. Chen and L. G. He, A new characterization o Simple K₄ -group with type L₂(p), Advances in Mathematics (China), (2012), doi: 10.11845/sxjz.165b
Search in Google Scholar Back to article
[5] B. Ebrahimzadeh, A. Iranmanesh, A. Tehranian, and H. Parvizi Mosaed, 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
Search in Google Scholar Back to article
[6] B. Ebrahimzadeh and R. Mohammadyari, A new characterization of projective special unitary groups PSU₃(3ⁿ), Discussiones Mathematicae General Algebra and Applications, 39, (2019), 35-4110.7151/dmgaa.1305
Search in Google Scholar Back to article
[7] B. Ebrahimzadeh, M. Y. Sadeghi, A. Iranmanesh, and A. Tehranian,A new characterization of symplectics groups PSP (8, q), An. S¸tiint¸. Univ. Al. I. Cuza Iaşi. Mat. (N.S.), LXVI (1), (2020), 93-99
Search in Google Scholar Back to article
[8] B. Ebrahimzadeh, R. Mohammadyari, and M. Y. Sadeghi,ANewCharacterization 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)10.12697/ACUTM.2019.23.24
Search in Google Scholar Back to article
[9] D. Gorenstein, Finite groups, Harper and Row, New York, 1980
Search in Google Scholar Back to article
[10] L. G. He and 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
Search in Google Scholar Back to article
[11] W. M. Kantor and A. Seress, Large element orders and the characteristic of Lie-type simple groups, J. Algebra, 322, (2009), 802-83210.1016/j.jalgebra.2009.05.004
Search in Google Scholar Back to article
[12] A. Khosravi and B. Khosravi, A new characterization of some alternting and symmetric groups, Int. J. Math. and Math. Sci, (2003), 2863-287210.1155/S0161171203202386
Search in Google Scholar Back to article
[13] J. Li, W. Shi, and D. Yu, A characterization of some PGL(2, q) by maximum element orders, Bull.Korean Math.Soc, 52 (6), (2015), 2025-203410.4134/BKMS.2015.52.6.2025
Search in Google Scholar Back to article
[14] J. S. Williams, Prime graph components of finite groups, J. Algebra, 69 (2), (1981), 487-51310.1016/0021-8693(81)90218-0
Search in Google Scholar Back to article
[15] D. Yu, J. Li, G. Chen, L. Zhang, and W. J. Shi, A new characterization of simple K₅-groups of type L₃(p), Bulletin of the Iranian Mathematical Society, 45 (3), (2019), 771-78110.1007/s41980-018-0164-0
Search in Google Scholar Back to article
[16] A. V. Zavarnitsine, Recognition of the simple groups L₃(q) by element orders, J. Group Theory, 7 (1), (2004), 81-9710.1515/jgth.2003.044
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/awutm-2019-0014 | Journal eISSN: 1841-3307 | Journal ISSN: 1841-3293

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Language: English

Page range: 53 - 60

Published on: Dec 21, 2020

Published by: West University of Timisoara

In partnership with: Paradigm Publishing Services

Publication frequency: Volume open

Keywords:

elements order,

largest element order,

prime graph

Related subjects:

Mathematics,

General mathematics

© 2020 Behnam Ebrahimzadeh, published by West University of Timisoara
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 57 (2019): Issue 2 (December 2019)