Geodesic
Insolubility of finite groups which are isospectral to the alternating group of degree~$10$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 5 (2008), pp. 20-24.

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $G$ be a finite group and $\omega(G)$ the set of all element orders of $G$. We prove that if $\omega(G)=\omega(A_{10})$ where $G$ is a finite group, then $G$ is not-soluble. 
@article{SEMR_2008_5_a3,
     author = {A. M. Staroletov},
     title = {Insolubility of finite groups which are isospectral to the alternating group of degree~$10$},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {20--24},
     publisher = {mathdoc},
     volume = {5},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2008_5_a3/}
}
TY  - JOUR
AU  - A. M. Staroletov
TI  - Insolubility of finite groups which are isospectral to the alternating group of degree~$10$
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2008
SP  - 20
EP  - 24
VL  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2008_5_a3/
LA  - ru
ID  - SEMR_2008_5_a3
ER  - 
%0 Journal Article
%A A. M. Staroletov
%T Insolubility of finite groups which are isospectral to the alternating group of degree~$10$
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2008
%P 20-24
%V 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2008_5_a3/
%G ru
%F SEMR_2008_5_a3
A. M. Staroletov. Insolubility of finite groups which are isospectral to the alternating group of degree~$10$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 5 (2008), pp. 20-24. http://geodesic.mathdoc.fr/item/SEMR_2008_5_a3/

[1] Lucido M. S., Moghaddamfar A. R., “Groups with complete prime graph connected components”, J. Group Theory, 7:3 (2004), 373–384 | DOI | MR | Zbl

[2] Aleeva M. R., “O konechnykh prostykh gruppakh s mnozhestvom poryadkov elementov kak u gruppy Frobeniusa ili dvoinoi gruppy Frobeniusa”, Matem. zametki, 73:3 (2003), 323–339 | MR | Zbl

[3] Mazurov V. D., “Gruppy s zadannym spektrom”, Izvestiya Uralskogo gosudarstvennogo universiteta, Matematika i mekhanika, 36:7 (2005), 119–138 | MR | Zbl

[4] Williams J. S., “Prime graph components of finite groups”, J. Algebra, 69:2 (1981), 487–513 | DOI | MR | Zbl

[5] Gorenstein D., Finite Groups, 2nd ed., Chelsea, New York, 1980 | MR | Zbl

[6] Zavarnitsin A. V., Mazurov V. D., “O poryadkakh elementov v nakrytiyakh simmetricheskikh i znakoperemenykh grupp”, Algebra i logika, 38:3 (1999), 296–315 ; 567–585 | MR

[7] Kargapolov M. I., Merzlyakov Yu. I., Osnovy teorii grupp, 4-e izd., pererab., Nauka. Fizmatlit, M., 1996, 288 pp. | MR | Zbl