The graph of atomic divisors and recognition of finite simple groups

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The graph of atomic divisors and recognition of finite simple groups. / Buturlakin, Alexander A.; Vasil'ev, Andrey V.

In: Journal of Algebra, Vol. 537, 01.11.2019, p. 478-502.

Research output: Contribution to journal › Article › peer-review

BibTeX

@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.}",

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.",

}

RIS

TY - JOUR

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

AU - Buturlakin, Alexander A.

AU - Vasil'ev, Andrey V.

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 -

ID: 21240086