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arXiv · 0807.2207

On Sun's conjecture concerning disjoint cosets

Wan-Jie Zhu
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Abstract

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.

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Wan-Jie Zhu. 2008-07-14. On Sun's conjecture concerning disjoint cosets. https://arxiv.org/abs/0807.2207

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