| Title:
|
A new characterization of Suzuki groups (English) |
| Author:
|
Ebrahimzadeh, Behnam |
| Author:
|
Mohammadyari, Reza |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
55 |
| Issue:
|
1 |
| Year:
|
2019 |
| Pages:
|
17-21 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
One of the important questions that remains after the classification of the finite simple groups is how to recognize a simple group via specific properties. For example, authors have been able to use graphs associated to element orders and to number of elements with specific orders to determine simple groups up to isomorphism. In this paper, we prove that Suzuki groups $Sz(q)$, where $q\pm \sqrt{2q}+1$ is a prime number can be uniquely determined by the order of group and the number of elements with the same order. (English) |
| Keyword:
|
element order |
| Keyword:
|
prime graph |
| Keyword:
|
Suzuki group |
| MSC:
|
20D06 |
| MSC:
|
20D60 |
| idZBL:
|
Zbl 07088754 |
| idMR:
|
MR3939060 |
| DOI:
|
10.5817/AM2019-1-17 |
| . |
| Date available:
|
2019-03-23T12:19:09Z |
| Last updated:
|
2020-02-27 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147646 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] Frobenius, G.: Verallgemeinerung des Sylowschen Satze.Berliner Sitz (1895), 981–983. |
| Reference:
|
[4] Gorenstein, D.: Finite Groups.Harper and Row, New York, 1980. Zbl 0463.20012, MR 0569209 |
| Reference:
|
[5] Khalili Asboei, A., Amiri, S.S., Iranmanesh, A., Tehranian, A.: A new characterization of sporadic simple groups by NSE and order.J. Algebra Appl. 12 (2) (2013), 1250158. MR 3005607, 10.1142/S0219498812501587 |
| Reference:
|
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| Reference:
|
[7] Parvizi Mosaed, H., Iranmanesh, A., 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:
|
[8] Shao, C.G., Shi, W., Jiang, Q.H.: Characterization of simple $K_4$-groups.Front Math. China 3 (3) (2008), 355–370. Zbl 1165.20020, MR 2425160, 10.1007/s11464-008-0025-x |
| Reference:
|
[9] Suzuki, M.: On a class of doubly transitive groups.Ann. of Math. 2 (75) (1962), 105–145. MR 0136646, 10.2307/1970423 |
| Reference:
|
[10] Wiliams, J.S.: Prime graph components of finite groups.J. Algebra 69 (2) (1981), 487–512. MR 0617092, 10.1016/0021-8693(81)90218-0 |
| . |
