NON-FACTORIZABLE GROUPS - Darafsheh, M.R.; Rezaeezadeh, G.R.; Koruki, M.R. Dehghan (Italian Journal of Pure and Applied Mathematics, 2013)
A group G is called a factorizable group if there are proper subgroups A and B of G such that G = AB. If G is non-trivial and no such a factorization exists G is called a non-factorizable group. In this paper we will show that if G is a non-factorizable group with Frattini subgroup as a minimal normal subgroup of order pn, (1 ≤ n ≤ 5), where p is a prime number, then G is a quasi-simple group.