Geodesic
A new characterization of symmetric group by NSE
Czechoslovak Mathematical Journal, Tome 67 (2017) no. 2, pp. 427-437.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

Let $G$ be a group and $\omega (G)$ be the set of element orders of $G$. Let $k\in \omega (G)$ and $m_k(G)$ be the number of elements of order $k$ in $G$. Let nse$(G) = \{m_k(G) \colon k \in \omega (G)\}$. Assume $r$ is a prime number and let $G$ be a group such that nse$(G)=$ nse$(S_r)$, where $S_r$ is the symmetric group of degree $r$. In this paper we prove that $G\cong S_r$, if $r$ divides the order of $G$ and $r^2$ does not divide it. To get the conclusion we make use of some well-known results on the prime graphs of finite simple groups and their components.
DOI : 10.21136/CMJ.2017.0700-15
Classification : 20D06, 20D15
Keywords: set of the numbers of elements of the same order; prime graph 
@article{10_21136_CMJ_2017_0700_15,
     author = {Babai, Azam and Akhlaghi, Zeinab},
     title = {A new characterization of symmetric group by {NSE}},
     journal = {Czechoslovak Mathematical Journal},
     pages = {427--437},
     publisher = {mathdoc},
     volume = {67},
     number = {2},
     year = {2017},
     doi = {10.21136/CMJ.2017.0700-15},
     mrnumber = {3661051},
     zbl = {06738529},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2017.0700-15/}
}
TY  - JOUR
AU  - Babai, Azam
AU  - Akhlaghi, Zeinab
TI  - A new characterization of symmetric group by NSE
JO  - Czechoslovak Mathematical Journal
PY  - 2017
SP  - 427
EP  - 437
VL  - 67
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2017.0700-15/
DO  - 10.21136/CMJ.2017.0700-15
LA  - en
ID  - 10_21136_CMJ_2017_0700_15
ER  - 
%0 Journal Article
%A Babai, Azam
%A Akhlaghi, Zeinab
%T A new characterization of symmetric group by NSE
%J Czechoslovak Mathematical Journal
%D 2017
%P 427-437
%V 67
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2017.0700-15/
%R 10.21136/CMJ.2017.0700-15
%G en
%F 10_21136_CMJ_2017_0700_15
Babai, Azam; Akhlaghi, Zeinab. A new characterization of symmetric group by NSE. Czechoslovak Mathematical Journal, Tome 67 (2017) no. 2, pp. 427-437. doi : 10.21136/CMJ.2017.0700-15. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2017.0700-15/

Cité par Sources :