Let G be a finite group. The spectrum of G is the set of all its element orders. The Gruenberg-Kegel graph (the prime 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, any finite simple group is recognizable by its spectrum and its order. 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, in particular, we discuss questions of recodnazibllity of a finite groups by its spectrum, by its Gruenberg-Kegel graph, and by some its other arithmetic invariants.
Natalia Maslova，2019年获俄罗斯数学科学博士学位，并获得Cheryl E. Praeger访问研究奖学金。现为乌拉尔联邦大学的教授，俄罗斯科学院乌拉尔分院克拉索夫斯基数学和力学研究所首席研究员，研究领域包含群论和组合学。