Glasgow Mathematical Journal

Research Article

FACTORIZATION NUMBERS OF SOME FINITE GROUPS

F. SAEEDIa1 and M. FARROKHI D. G.a2

a1 Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran. e-mail: saeedi@mshdiau.ac.ir

a2 Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran. e-mail: m.farrokhi.d.g@gmail.com

Abstract

For a finite group G, let F2(G) be the number of factorizations G = AB of the group G, where A and B are subgroups of G. We compute F2(G) for certain classes of groups, including cyclic groups ℤn, elementary abelian p-groups ℤpn, dihedral groups D2n, generalised quaternion groups Q4n, quasi-dihedral 2-groups QD2n(n≥4), modular p-groups Mpn, projective general linear groups PGL(2, pn) and projective special linear groups PSL(2, pn).

(Received August 16 2011)

(Accepted September 24 2011)

(Online publication December 12 2011)

2000 Mathematics Subject Classification

  • Primary 20D40;
  • secondary 20P05