A Characterization of Projective Special Unitary Group U3(7) by nse. (22nd August 2013)

• Record Type: Journal Article
• Authors: Liu, Shitian
• Other Names: Yang Shilin Academic Editor.
• Is Part Of: Algebra. Volume 2013(2013)
• Publication Date: 2013-08-22
• Subjects: Algebra -- Periodicals; Algebra; Electronic journals; Periodicals; 512.005
• DOI: 10.1155/2013/983186
• Languages: English
• ISSNs: 2314-4106

Abstract

Abstract : Let G a group and ω ( G ) be the set of element orders of G . Let k ∈ ω ( G ) and let s k be the number of elements of order k in G . Let nse( G ) = { s k ∣ k ∈ ω ( G ) } . In Khatami et al. and Liu's works, L 3 ( 2 ) and L 3 ( 4 ) are uniquely determined by nse( G ) . In this paper, we prove that if G is a group such that nse( G ) = nse( U 3 ( 7 ) ), then G ≅ U 3 ( 7 ) .