SOME QUANTITATIVE CHARACTERIZATIONS OF CERTAIN SYMPLECTIC GROUPS OVER THE BINARY FIELD

Authors : M Akbari, A R Moghaddamfar

Pages : 32-52

Doi:10.24330/ieja.266225

View : 9 | Download : 5

Publication Date : 2014-12-01

Article Type : Research Paper

Abstract :Given a finite group G, denote by Dinsert ignore into journalissuearticles values(G); the degree pattern of G and by OCinsert ignore into journalissuearticles values(G); the set of all order components of G. Denote by hODinsert ignore into journalissuearticles values(G); insert ignore into journalissuearticles values(resp. hOCinsert ignore into journalissuearticles values(G);); the number of isomorphism classes of finite groups H satisfying conditions |H| = |G| and Dinsert ignore into journalissuearticles values(H); = Dinsert ignore into journalissuearticles values(G); insert ignore into journalissuearticles values(resp. OCinsert ignore into journalissuearticles values(H); = OCinsert ignore into journalissuearticles values(G););. A finite group G is called OD-characterizable insert ignore into journalissuearticles values(resp. OC-characterizable); if hODinsert ignore into journalissuearticles values(G); = 1 insert ignore into journalissuearticles values(resp. hOCinsert ignore into journalissuearticles values(G); = 1);. Let C = Cpinsert ignore into journalissuearticles values(2); be a symplectic group over the binary field, for which 2p − 1 > 7 is a Mersenne prime. The aim of this article is to prove that hODinsert ignore into journalissuearticles values(C); = 1 = hOCinsert ignore into journalissuearticles values(C);.
Keywords : Spectrum of a group, prime graph, degree pattern, order component, symplectic group Cn q, OD OC, characterizability of a finite group