Some Quantitative Characterizations of Certain Symplectic Groups Over the Binary Field

Abstract

Abstract. Given a finite group G, denote by D(G) the degree pattern of G and by OC(G) the set of all order components of G. Denote by h OD (G) (resp. h OC (G)) the number of isomorphism classes of finite groups H satisfying conditions |H| = |G| and D(H) = D(G) (resp. OC(H) = OC(G)). A finite group G is called OD-characterizable (resp. OC-characterizable) if h OD (G) = 1 (resp. h OC (G) = 1). Let C = Cp(2) be a symplectic group over the binary field, for which 2 p − 1 > 7 is a Mersenne prime. The aim of this article is to prove that h OD (C) = 1 = h OC (C).

OD-characterization of alternating groups Ap+d

“…For the groups which are k-fold OD-characterizable, please see Tables 1 and 2 and corresponding references of [3]. Many finite groups are k-fold OD-characterizable.…”

OD-characterization of some alternating groups

“…Moghaddamfar et al introduced the following concept, which attracted the attention of some authors (see [1]). Definition 1.1 [12] Let G be a finite group and |G| = p α1 1 p α2 2 • • • p α k k , where p i s are primes and α i s are integers.…”

“…To date, we knew that some groups are k -fold OD -characterizable (see Tables 1 and 2 and corresponding references of [1]). …”