## Expansion of coset graphs of PSL_2(F_p). (arXiv:1810.09925v1 [math.GR])

Let \$G\$ be a finite group and let \$H_1,H_2&lt;G\$ be two subgroups. In this paper, we are concerned with the bipartite graph whose vertices are \$G/H_1\cup G/H_2\$ and a coset \$g_1H_1\$ is connected with another coset \$g_2H_2\$ if and only if \$g_1H_1\cap g_2 H_2\neq\varnothing\$. The main result of the paper establishes the existence of such graphs with large girth and large spectral gap. Lubotzky, Manning and Wilton use such graphs to construct certain infinite groups of interest in geometric group theory.查看全文

## Solidot 文章翻译

 你的名字 留空匿名提交 你的Email或网站 用户可以联系你 标题 简单描述 内容 Let \$G\$ be a finite group and let \$H_1,H_2<G\$ be two subgroups. In this paper, we are concerned with the bipartite graph whose vertices are \$G/H_1\cup G/H_2\$ and a coset \$g_1H_1\$ is connected with another coset \$g_2H_2\$ if and only if \$g_1H_1\cap g_2 H_2\neq\varnothing\$. The main result of the paper establishes the existence of such graphs with large girth and large spectral gap. Lubotzky, Manning and Wilton use such graphs to construct certain infinite groups of interest in geometric group theory.
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