| Title:
|
Recognizability of finite groups by Suzuki group (English) |
| Author:
|
Asboei, Alireza Khalili |
| Author:
|
Amiri, Seyed Sadegh Salehi |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
55 |
| Issue:
|
4 |
| Year:
|
2019 |
| Pages:
|
225-228 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $q=2^{2m+1}\ge 8$. (English) |
| Keyword:
|
main supergraph |
| Keyword:
|
Suzuki group |
| MSC:
|
05C25 |
| MSC:
|
20D08 |
| idZBL:
|
Zbl 07144737 |
| idMR:
|
MR4038357 |
| DOI:
|
10.5817/AM2019-4-225 |
| . |
| Date available:
|
2019-10-30T08:52:19Z |
| Last updated:
|
2020-04-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147875 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[5] Iranmanesh, A., Parvizi, H., Tehranian, A.: Characterization of Suzuki group by NSE and order of group.Bull. Korean Math. Soc. 53 (3) (2016), 651–656. MR 3508660, 10.4134/BKMS.b140564 |
| Reference:
|
[6] Khalili, A., Salehi, S.S.: Some results on the main supergraph of finite groups.Accepted in Algebra Discrete Math. |
| Reference:
|
[7] Khalili, A., Salehi, S.S.: Some alternating and symmetric groups and related graphs.Beitr. Algebra Geom. 59 (2018), 21–24. MR 3761396, 10.1007/s13366-017-0360-8 |
| Reference:
|
[8] Khalili, A., Salehi, S.S.: The small Ree group $^{2}G_{2}(3^{2n+1})$ and related graph.Comment. Math. Univ. Carolin. 59 (3) (2018), 271–276. MR 3861551 |
| Reference:
|
[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. MR 3408705 |
| Reference:
|
[10] Salehi, S.S., Khalili, A.: Recognition of $L_{2}(q)$ by the main supergraph.Accepted in Iran. J. Math. Sci. Inform. |
| Reference:
|
[11] Shi, W.J.: A characterization of Suzuki’s simple groups.Proc. Amer. Math. Soc. 114 (3) (1992), 589–591. MR 1074758, 10.1090/S0002-9939-1992-1074758-0 |
| Reference:
|
[12] Williams, J.S.: Prime graph components of finite groups.J. Algebra 69 (2) (1981), 487–513. Zbl 0471.20013, MR 0617092, 10.1016/0021-8693(81)90218-0 |
| . |
