Finite solvable groups whose Gruenberg-Kegel graphs are isomorphic to the paw
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 28 (2022) no. 2, pp. 269-273
Voir la notice de l'article provenant de la source Math-Net.Ru
The Gruenberg-Kegel graph (or the prime graph) of a finite group $G$ is the graph, in which the vertex set is the set of all prime divisors of the order of $G$ and two different vertices $p$ and $q$ are adjacent if and only if there exists an element of order $pq$ in $G$. The paw is the graph on four vertices whose degrees are 1, 2, 2, and 3. We consider the problem of describing finite groups whose Gruenberg-Kegel graphs are isomorphic as abstract graphs to the paw. For example, the Gruenberg-Kegel graphs of the groups $A_{10}$ and $\mathrm{Aut}(J_2)$ are isomorphic as abstract graphs to the paw. In this paper, we describe finite solvable groups whose Gruenberg-Kegel graphs are isomorphic as abstract graphs to the paw.
Keywords:
finite group; solvable group; Gruenberg-Kegel graph; paw.
@article{TIMM_2022_28_2_a20,
author = {A. S. Kondrat'ev and N. A. Minigulov},
title = {Finite solvable groups whose {Gruenberg-Kegel} graphs are isomorphic to the paw},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {269--273},
publisher = {mathdoc},
volume = {28},
number = {2},
year = {2022},
language = {en},
url = {http://geodesic.mathdoc.fr/item/TIMM_2022_28_2_a20/}
}
TY - JOUR AU - A. S. Kondrat'ev AU - N. A. Minigulov TI - Finite solvable groups whose Gruenberg-Kegel graphs are isomorphic to the paw JO - Trudy Instituta matematiki i mehaniki PY - 2022 SP - 269 EP - 273 VL - 28 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TIMM_2022_28_2_a20/ LA - en ID - TIMM_2022_28_2_a20 ER -
%0 Journal Article %A A. S. Kondrat'ev %A N. A. Minigulov %T Finite solvable groups whose Gruenberg-Kegel graphs are isomorphic to the paw %J Trudy Instituta matematiki i mehaniki %D 2022 %P 269-273 %V 28 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/TIMM_2022_28_2_a20/ %G en %F TIMM_2022_28_2_a20
A. S. Kondrat'ev; N. A. Minigulov. Finite solvable groups whose Gruenberg-Kegel graphs are isomorphic to the paw. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 28 (2022) no. 2, pp. 269-273. http://geodesic.mathdoc.fr/item/TIMM_2022_28_2_a20/