SOME QUANTITATIVE CHARACTERIZATIONS OF CERTAIN SYMPLECTIC GROUPS OVER THE BINARY FIELD

Year 2014, Volume: 16 Issue: 16, 32 - 52, 01.12.2014

M. Akbari A. R. Moghaddamfar

https://doi.org/10.24330/ieja.266225

Cited By: 1

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 hOD(G) (resp.
hOC(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 hOD(G) = 1 (resp.
hOC(G) = 1). Let C = Cp(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
hOD(C) = 1 = hOC(C).

Keywords

Spectrum of a group, prime graph, degree pattern, order component, symplectic group Cn(q), OD(OC)-characterizability of a finite group