@article{f856869227554ebdac35a8aff9d37cf2,
title = "The graph of atomic divisors and recognition of finite simple groups",
abstract = "The spectrum ω(G) of a finite group G is the set of orders of elements of G. We present a polynomial-time algorithm that, given a finite set M of positive integers, outputs either an empty set or a finite simple group G. In the former case, there is no finite simple group H with M=ω(H), while in the latter case, M⊆ω(G) and M≠ω(H) for all finite simple groups H with ω(H)≠ω(G).",
keywords = "Finite simple group, Graph of atomic divisors, Polynomial-time algorithms, Prime graph, Recognition by spectrum, Spectrum of a group, ELEMENT, PRIME GRAPH",
author = "Buturlakin, {Alexander A.} and Vasil'ev, {Andrey V.}",
note = "Publisher Copyright: {\textcopyright} 2019 Elsevier Inc. Copyright: Copyright 2019 Elsevier B.V., All rights reserved.",
year = "2019",
month = nov,
day = "1",
doi = "10.1016/j.jalgebra.2019.07.013",
language = "English",
volume = "537",
pages = "478--502",
journal = "Journal of Algebra",
issn = "0021-8693",
publisher = "Academic Press Inc.",
}