Recognizability of finite groups by Suzuki group

Alireza Khalili Asboei; Seyed Sadegh Salehi Amiri

Archivum Mathematicum (2019)

  • Volume: 055, Issue: 4, page 225-228
  • ISSN: 0044-8753

Abstract

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Let G be a finite group. The main supergraph 𝒮 ( G ) is a graph with vertex set G in which two vertices x and y are adjacent if and only if o ( x ) ∣ o ( y ) or o ( y ) ∣ o ( x ) . In this paper, we will show that G ≅ S z ( q ) if and only if 𝒮 ( G ) ≅ 𝒮 ( S z ( q ) ) , where q = 2 2 m + 1 ≥ 8 .

How to cite

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Asboei, Alireza Khalili, and Amiri, Seyed Sadegh Salehi. "Recognizability of finite groups by Suzuki group." Archivum Mathematicum 055.4 (2019): 225-228. <http://eudml.org/doc/294366>.

@article{Asboei2019,
abstract = {Let $G$ be a finite group. The main supergraph $\mathcal \{S\}(G)$ is a graph with vertex set $G$ in which two vertices $x$ and $y$ are adjacent if and only if $o(x) \mid o(y)$ or $o(y)\mid o(x)$. In this paper, we will show that $G\cong Sz(q)$ if and only if $\mathcal \{S\}(G)\cong \mathcal \{S\}(Sz(q))$, where $q=2^\{2m+1\}\ge 8$.},
author = {Asboei, Alireza Khalili, Amiri, Seyed Sadegh Salehi},
journal = {Archivum Mathematicum},
keywords = {main supergraph; Suzuki group},
language = {eng},
number = {4},
pages = {225-228},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Recognizability of finite groups by Suzuki group},
url = {http://eudml.org/doc/294366},
volume = {055},
year = {2019},
}

TY - JOUR
AU - Asboei, Alireza Khalili
AU - Amiri, Seyed Sadegh Salehi
TI - Recognizability of finite groups by Suzuki group
JO - Archivum Mathematicum
PY - 2019
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 055
IS - 4
SP - 225
EP - 228
AB - Let $G$ be a finite group. The main supergraph $\mathcal {S}(G)$ is a graph with vertex set $G$ in which two vertices $x$ and $y$ are adjacent if and only if $o(x) \mid o(y)$ or $o(y)\mid o(x)$. In this paper, we will show that $G\cong Sz(q)$ if and only if $\mathcal {S}(G)\cong \mathcal {S}(Sz(q))$, where $q=2^{2m+1}\ge 8$.
LA - eng
KW - main supergraph; Suzuki group
UR - http://eudml.org/doc/294366
ER -

References

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  1. Alavi, H., Daneshkhah, A., Parvizi, H., Groups of the same type as Suzuki groups, Int. J. Group Theory 8 (1) (2019), 35–42. (2019) MR3953262
  2. Chen, G.Y., On Frobenius and 2 -Frobenius group, J. Southwest China Normal Univ. 20 (1995), 485–487, in Chinese. (1995) 
  3. Glauberman, G., Factorizations in local subgroups of finite groups, Regional Conference Series in Mathematics, no. 33, American Mathematical Society, Providence, R.I., 1977. (1977) MR0470072
  4. Hamzeh, A., Ashrafi, A.R., 10.1016/j.ejc.2016.09.005, European J. Combin. 60 (2017), 82–88. (2017) MR3567537DOI10.1016/j.ejc.2016.09.005
  5. Iranmanesh, A., Parvizi, H., Tehranian, A., 10.4134/BKMS.b140564, Bull. Korean Math. Soc. 53 (3) (2016), 651–656. (2016) MR3508660DOI10.4134/BKMS.b140564
  6. Khalili, A., Salehi, S.S., Some results on the main supergraph of finite groups, Accepted in Algebra Discrete Math. 
  7. Khalili, A., Salehi, S.S., 10.1007/s13366-017-0360-8, Beitr. Algebra Geom. 59 (2018), 21–24. (2018) MR3761396DOI10.1007/s13366-017-0360-8
  8. Khalili, A., Salehi, S.S., The small Ree group 2 G 2 ( 3 2 n + 1 ) and related graph, Comment. Math. Univ. Carolin. 59 (3) (2018), 271–276. (2018) MR3861551
  9. Mazurov, V.D., Khukhro, E.I., Unsolved problems in group theory, The Kourovka Notebook, (English version), ArXiv e-prints, (18), January 2014. Available at http://arxiv.org/abs/1401.0300v6. MR3408705
  10. Salehi, S.S., Khalili, A., Recognition of L 2 ( q ) by the main supergraph, Accepted in Iran. J. Math. Sci. Inform. 
  11. Shi, W.J., 10.1090/S0002-9939-1992-1074758-0, Proc. Amer. Math. Soc. 114 (3) (1992), 589–591. (1992) MR1074758DOI10.1090/S0002-9939-1992-1074758-0
  12. Williams, J.S., 10.1016/0021-8693(81)90218-0, J. Algebra 69 (2) (1981), 487–513. (1981) Zbl0471.20013MR0617092DOI10.1016/0021-8693(81)90218-0

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