  In 2004, Zhi-Wei Sun posed the following conjecture: If a_1G_1,...,a_kG_k
(k>1) are finitely many pairwise disjoint left cosets in a group G with all the
indices [G:G_i] finite, then for some 1\le i<j\le k, the greatest common
divisor of [G:G_i] and [G:G_j] is at least k. In this paper, we confirm Sun's
conjecture for k=3,4.
