FACTORIZATION NUMBERS OF SOME FINITE GROUPS

Abstract

AbstractFor 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).