A new characterization of symmetric groups for some n

Authors : Alireza Khalili ASBOEİ, , Seyed Sadegh Salehi AMİRİ, Ali IRANMANESH

Pages : 715-723

View : 13 | Download : 6

Publication Date : 2014-10-01

Article Type : Research Paper

Abstract :Let G be a finite group and let πeinsert ignore into journalissuearticles values(G); be the set of element orders G. Let k ∈ πeinsert ignore into journalissuearticles values(G); and let mk be the number of elements of order k in G. Set nseinsert ignore into journalissuearticles values(G);:={mk|k ∈ πeinsert ignore into journalissuearticles values(G);}. In this paper, we prove that if G is a group such that nseinsert ignore into journalissuearticles values(G);=nseinsert ignore into journalissuearticles values(Sn); where n ∈ {3, 4, 5, 6, 7}, then G ∼= Sn.
Keywords : Symmetric group, element order, set of the numbers of elements of the same order