TY - JOUR

T1 - The graph of atomic divisors and recognition of finite simple groups

AU - Buturlakin, Alexander A.

AU - Vasil'ev, Andrey V.

N1 - Publisher Copyright: © 2019 Elsevier Inc. Copyright: Copyright 2019 Elsevier B.V., All rights reserved.

PY - 2019/11/1

Y1 - 2019/11/1

N2 - 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).

AB - 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).

KW - Finite simple group

KW - Graph of atomic divisors

KW - Polynomial-time algorithms

KW - Prime graph

KW - Recognition by spectrum

KW - Spectrum of a group

KW - ELEMENT

KW - PRIME GRAPH

UR - http://www.scopus.com/inward/record.url?scp=85070686329&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2019.07.013

DO - 10.1016/j.jalgebra.2019.07.013

M3 - Article

AN - SCOPUS:85070686329

VL - 537

SP - 478

EP - 502

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -