A characterization of symplectic groups related to Fermat primes

Behnam Ebrahimzadeh; Alireza K. Asboei

Commentationes Mathematicae Universitatis Carolinae (2021)

  • Issue: 1, page 33-40
  • ISSN: 0010-2628

Abstract

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We proved that the symplectic groups PSp ( 4 , 2 n ) , where 2 2 n + 1 is a Fermat prime number is uniquely determined by its order, the first largest element orders and the second largest element orders.

How to cite

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Ebrahimzadeh, Behnam, and Asboei, Alireza K.. "A characterization of symplectic groups related to Fermat primes." Commentationes Mathematicae Universitatis Carolinae (2021): 33-40. <http://eudml.org/doc/298001>.

@article{Ebrahimzadeh2021,
abstract = {We proved that the symplectic groups $\mathrm \{PSp\}(4,2^\{n\})$, where $2^\{2n\}+1$ is a Fermat prime number is uniquely determined by its order, the first largest element orders and the second largest element orders.},
author = {Ebrahimzadeh, Behnam, Asboei, Alireza K.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {element order; the largest element order; prime graph; symplectic group},
language = {eng},
number = {1},
pages = {33-40},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A characterization of symplectic groups related to Fermat primes},
url = {http://eudml.org/doc/298001},
year = {2021},
}

TY - JOUR
AU - Ebrahimzadeh, Behnam
AU - Asboei, Alireza K.
TI - A characterization of symplectic groups related to Fermat primes
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2021
PB - Charles University in Prague, Faculty of Mathematics and Physics
IS - 1
SP - 33
EP - 40
AB - We proved that the symplectic groups $\mathrm {PSp}(4,2^{n})$, where $2^{2n}+1$ is a Fermat prime number is uniquely determined by its order, the first largest element orders and the second largest element orders.
LA - eng
KW - element order; the largest element order; prime graph; symplectic group
UR - http://eudml.org/doc/298001
ER -

References

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  1. Ebrahimzadeh B., Iranmanesh A., Tehranian A., Parvizi Mosaed H., A characterization of the Suzuki groups by order and the largest elements order, J. Sci. Islam. Repub. Iran 27 (2016), no. 4, 353–355. MR3581052
  2. Gorenstein D., Finite Groups, Chelsea Publishing Co., New York, 1980. Zbl0695.20014MR0569209
  3. He L.-G., Chen G.-Y., A new characterization of L 2 ( q ) where q = p n < 125 , Ital. J. Pure Appl. Math. 28 (2011), 127–136. MR2922488
  4. He L. G., Chen G. Y., A new characterization of L 3 ( q ) ( q ≤ 8 ) and U 3 ( q ) ( q ≤ 11 ) , J. Southwest China Normal Univ. 27(33) (2011), 81–87. MR1935864
  5. He L., Chen G., A new characterization of simple K 4 -groups with type L 2 ( p ) , Adv. Math. (China) 43 (2014), no. 5, 667–670. MR3291316
  6. He L.-G., Chen G.-Y., Xu H.-J., A new characterization of sporadic simple groups, Ital. J. Pure Appl. Math. 30 (2013), 373–392. MR3066520
  7. Kantor W. M., Seress Á., 10.1016/j.jalgebra.2009.05.004, J. Algebra 322 (2009), no. 3, 802–832. MR2531224DOI10.1016/j.jalgebra.2009.05.004
  8. Li J., Shi W., Yu D., 10.4134/BKMS.2015.52.6.2025, Bull. Korean Math. Soc. 52 (2015), no. 6, 2025–2034. MR3432734DOI10.4134/BKMS.2015.52.6.2025
  9. Vasil'ev A. V., Grechkoseeva M. A., Mazurov V. D., Characterization of finite simple groups by spectrum and order, Algebra Logika 48 (2009), no. 6, 685–728, 821, 824 (Russian. English, Russian summary); translation in Algebra Logic 48 (2009), no. 6, 385–409. MR2640961
  10. Williams J. S., 10.1016/0021-8693(81)90218-0, J. Algebra 69 (1981), no. 2, 487–513. Zbl0471.20013MR0617092DOI10.1016/0021-8693(81)90218-0

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