The graph of atomic divisors and recognition of finite simple groups

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

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).

Original languageEnglish
Pages (from-to)478-502
Number of pages25
JournalJournal of Algebra
Volume537
DOIs
Publication statusPublished - 1 Nov 2019

Keywords

  • Finite simple group
  • Graph of atomic divisors
  • Polynomial-time algorithms
  • Prime graph
  • Recognition by spectrum
  • Spectrum of a group
  • ELEMENT
  • PRIME GRAPH

Fingerprint

Dive into the research topics of 'The graph of atomic divisors and recognition of finite simple groups'. Together they form a unique fingerprint.

Cite this