A. L. Gavrilyuk, I. V. Khramtsov, A. S. Kondrat'ev, N. V. Maslova, “On realizability of a graph as the prime graph of a finite group”, Sib. Èlektron. Mat. Izv., 2014, Volume 11,Pages <nobr>246

This article is cited in 4 papers

Mathematical logic, algebra and number theory

On realizability of a graph as the prime graph of a finite group

A. L. Gavrilyuk^abc, I. V. Khramtsov^a, A. S. Kondrat'ev^ab, N. V. Maslova^ba

^a N. N. Krasovskii Institute of Mathematics and Mechanics, 16, S. Kovalevskaja St., 620990, Ekaterinburg, Russia
^b Ural Federal University named after the first President of Russia B. N. Yeltsin, 19, Mira St., 620002, Ekaterinburg, Russia
^c Research Center for Pure and Applied Mathematics, Graduate School of Information Sciences, Tohoku University, 980-8579, Sendai, Japan

Abstract: The problem of the realizability of a graph as the prime graph (the Gruenberg–Kegel graph) of a finite group is considered. This problem is completely solved for graphs with at most five vertices.

Keywords: finite group, prime graph (Gruenberg–Kegel graph), realizability of a graph.

UDC: 512.54

MSC: 20D60,05C25,20C20

Received November 14, 2013, published March 26, 2014

Language: English