ON THOMPSON'S CONJECTURE FOR ALTERNATING GROUP \(A_{26}\)

Shitian Liu; Yanhua Huang

ON THOMPSON'S CONJECTURE FOR ALTERNATING GROUP \(A_{26}\)

Autori

Shitian Liu Sichuan University of Science and Engineering - School of of Science
Yanhua Huang Sichuan University of Science and Engineering - School of of Science

Parole chiave:

element order, alternating group, thompson's conjecture, conjugacy classes, simple group

Abstract

Let G be a group. Denote by N(G) the set of nonidentity orders of conjugacy classes of elements in G. For groups A₁₀, A₁₆ and A₂₂which are uniquely determined by N(G), theses degrees are p+3 and p+4 is a prime with p = 7, 13, 19. If p+4 is composite, then whether can the groups A_p+₃ be characterized by N(G). In this paper, we give an example for A_p+3 with p+4 composite, namely, we proved that if G is a group with trivial center and N(G) = N(A₂₆), then G \(\cong\) A₂₆.

Cover of n°32 Italian Journal of Pure and Applied Mathematics

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Pubblicato

2014-08-22

Come citare

Liu, S., & Huang, Y. (2014). ON THOMPSON’S CONJECTURE FOR ALTERNATING GROUP \(A_{26}\). Italian Journal of Pure and Applied Mathematics, 32, 525–532. Recuperato da https://journals.uniurb.it/index.php/ijpam/article/view/6176