On Sun's conjecture concerning disjoint cosets
Abstract
In 2004, Zhi-Wei Sun posed the following conjecture: If a1G1,...,akGk (k>1) are finitely many pairwise disjoint left cosets in a group G with all the indices [G:Gi] finite, then for some 1 i<j k, the greatest common divisor of [G:Gi] and [G:Gj] is at least k. In this paper, we confirm Sun's conjecture for k=3,4.
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