A Characterization of Projective Special Unitary Group PSU(3,3) and Projective Special Linear Group PSL(3,3) by NSE

Farnoosh Hajati, Ali Iranmanesh and Abolfazl Tehranian
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Farnoosh Hajati: Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran 14515-775, Iran
Ali Iranmanesh: Department of Mathematics, Tarbiat Modares University, Tehran 14115-137, Iran
Abolfazl Tehranian: Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran 14515-775, Iran

Mathematics, 2018, vol. 6, issue 7, 1-10

Abstract: Let G be a finite group and ω ( G ) be the set of element orders of G . Let k ∈ ω ( G ) and m k be the number of elements of order k in G . Let n s e ( G ) = { m k | k ∈ ω ( G ) } . In this paper, we prove that if G is a finite group such that nse ( G ) = nse ( H ), where H = P S U ( 3 , 3 ) or P S L ( 3 , 3 ) , then G ≅ H .

Keywords: element order; number of elements of the same order; projective special linear group; projective special unitary group; simple K n -group (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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