Geodesic
On groups critical with respect to a set of natural numbers
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 666-675

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

The spectrum of a finite group is the set of its element orders. A finite group $G$ is critical with respect to a subset $\omega$ of natural numbers, if $\omega$ is equal to the spectrum of $G$ and not equal to the spectrum of any proper section of $G$. For any natural number $n$, we construct $n$ finite critical groups with the same spectrum. We also give a complete description of finite groups critical with respect to the spectrum of the alternating group of degree 6 and the spectrum of the special linear group of dimension 3 over a field of order 3.
Keywords: finite group, spectrum, critical group. 
@article{SEMR_2013_10_a18,
     author = {Yu. V. Lytkin},
     title = {On groups critical with respect to a set of natural numbers},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {666--675},
     publisher = {mathdoc},
     volume = {10},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2013_10_a18/}
}
TY  - JOUR
AU  - Yu. V. Lytkin
TI  - On groups critical with respect to a set of natural numbers
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2013
SP  - 666
EP  - 675
VL  - 10
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2013_10_a18/
LA  - en
ID  - SEMR_2013_10_a18
ER  - 
%0 Journal Article
%A Yu. V. Lytkin
%T On groups critical with respect to a set of natural numbers
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2013
%P 666-675
%V 10
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2013_10_a18/
%G en
%F SEMR_2013_10_a18
Yu. V. Lytkin. On groups critical with respect to a set of natural numbers. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 10 (2013), pp. 666-675. http://geodesic.mathdoc.fr/item/SEMR_2013_10_a18/