Previous |  Up |  Next

Article

Title: A new characterization of projective special unitary group PSU$(5, q)$ (English)
Author: Ebrahimzadeh, Behnam
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 65
Issue: 1
Year: 2024
Pages: 1-12
Summary lang: English
.
Category: math
.
Summary: Projective special unitary groups ${\rm PSU}(5,q)$, where $$ \frac{q^4-q^3+q^2-q+1}{(5,q+1)} $$ is a prime, is uniquely determined by its order and the size of one conjugacy class. (English)
Keyword: element order
Keyword: conjugacy class
Keyword: prime graph
Keyword: projective special unitary group
MSC: 20D06
MSC: 20D60
DOI: 10.14712/1213-7243.2024.015
.
Date available: 2025-04-24T07:42:50Z
Last updated: 2025-04-25
Stable URL: http://hdl.handle.net/10338.dmlcz/152938
.
Reference: [1] Amiri S. S. S., Asboei A. K.: Characterization of some finite groups by their order and by the length of a conjugacy class.Sibirsk. Mat. Zh. 57 (2016), no. 2, 241–246 (in Russian); translation in Sib. Math. J. 57 (2016), no. 2, 185–189. MR 3510189
Reference: [2] Asboei A. K.: Characterization of PSL$(5,q)$ by its order and one conjugacy class size.Iran. J. of Math. Sci. Inform. 15 (2020), no. 1, 35–40. MR 4108746
Reference: [3] Asboei A. K., Darafsheh M. R., Mohammadyari R.: The influence of order and conjugacy class length on the structure of finite groups.Hokkaido Math. J. 47 (2018), no. 1, 25–32. MR 3773724, 10.14492/hokmj/1520928059
Reference: [4] Asboei A. K., Mohammadyari R.: Characterization of the alternating groups by their order and one conjugacy class length.Czechoslovak Math. J. 66(141) (2016), no. 1, 63–70. MR 3483222, 10.1007/s10587-016-0239-0
Reference: [5] Asboei A. K., Mohammadyari R.: Recognizing alternating groups by their order and one conjugacy class length.J. Algebra. Appl. 15 (2016), no. 2, 1650021, 7 pages. MR 3405720
Reference: [6] Asboei A. K., Mohammadyari R., Rahimi-Esbo M.: New characterization of some linear groups.Int. J. Industrial Mathematics 8 (2016), no. 2, Article ID IJIM-00714, 6 pages.
Reference: [7] Chen G. Y.: On Frobenius and $2$-Frobenius group.J. Southwest China Norm. Univ. 20 (1995), no. 5, 485–487 (Chinese).
Reference: [8] Chen Y., Chen G.: Recognizing $L_2(p)$ by its order and one special conjugacy class size.J. Inequal. Appl. 2012 (2012), 2012:310, 10 pages. MR 3027693
Reference: [9] Chen Y., Chen G.: Recognition of $A_{10}$ and $L_4(4)$ by two special conjugacy class sizes.Ital. J. Pure Appl. Math. 29 (2012), 387–394. MR 3009613
Reference: [10] Darafsheh M. R.: Characterizability of the group $^3D_p(3)$ by its order components, where $ p \ge 5$ is a prime number not of the form $2^m + 1$.Acta Math. Sin. (Engl. Ser.) 24 (2008), no. 7, 1117–1126. MR 2420882, 10.1007/s10114-007-6143-7
Reference: [11] Gorenstein D.: Finite Groups.Chelsea Publishing Co., New York, 1980. Zbl 0695.20014, MR 0569209
Reference: [12] Iranmanesh A., Alavi S. H.: A characterization of simple group $PSL(5, q)$.Bull. Austral. Math. Soc. 65 (2002), 211–222. MR 1898535, 10.1017/S0004972700020256
Reference: [13] Kantor W. M., Seress Á.: Large element orders and the characteristic of Lie-type simple groups.J. Algebra 322 (2009), no. 3, 802–832. MR 2531224, 10.1016/j.jalgebra.2009.05.004
Reference: [14] Mazurov V. D., Khukhro E. I.: Unsolved Problems in Group Theory, The Kourovka Notebook.16 ed., Inst. Mat. Sibirsk. Otdel. Akad., Novosibirsk, 2006. MR 2263886
Reference: [15] Wall E. G.: On the conjugacy classes in the unitary, symplectic and orthogonal groups.J. Aust. Math. Soc. 3 (1963), no. 1, 1–62. MR 0150210, 10.1017/S1446788700027622
Reference: [16] Williams J. S.: Prime graph components of finite groups.J. Algebra 69 (1981), no. 2, 487–513. Zbl 0471.20013, MR 0617092, 10.1016/0021-8693(81)90218-0
Reference: [17] Zavarnitsine A. V.: Recognition of the simple groups $L_3(q)$ by element orders.J. Group Theory 7 (2004), no. 1, 81–97. MR 2030231
.

Fulltext not available (moving wall 24 months)

Partner of
EuDML logo