SEMINAR: Groups and Combinatorics Seminar: Natalia Maslova, 4pm Oct 18 in Weatherburn LT

Speaker: Natalia Maslova (Ural Federal University)

Title: On Gruenberg-Kegel graphs of finite groups

Time and place: 4pm Friday 18 Oct 2019, Weatherburn LT

Abstract: Let G be a finite group. The spectrum of G is the set of all its element orders. The Gruenberg-Kegel graph of G is a graph whose vertex set is the set of all prime divisors of the order of G, and two distinct vertices are adjacent in this graph if and only if their product is an element order of G. The spectrum is a very important invariant of a finite group. For example, many finite simple groups are defined by their spectra up to isomorphism. The concept of the Gruenberg-Kegel graph of a finite group widely generalizes the concept of the spectrum. In this talk we discuss some characterizations of finite groups by properties of their spectra and Gruenberg-Kegel graphs.