论文标题
通过次要排除的几乎免费组的表征
A characterisation of virtually free groups via minor exclusion
论文作者
论文摘要
我们使用图形未成年人给出了几乎免费组的新表征。也就是说，我们证明，当并且仅当对于任何有限生成集时，几乎有限生成的无限基团是免费的，相应的cayley图被较小。这回答了Ostrovskii和Rosenthal的问题。证明依赖于证明，使用图形理论表征Thomassen和Woess引起的图形理论表征，可访问一个有限生成的相对于每个有限生成集的有限生成的组。
We give a new characterisation of virtually free groups using graph minors. Namely, we prove that a finitely generated, infinite group is virtually free if and only if for any finite generating set, the corresponding Cayley graph is minor excluded. This answers a question of Ostrovskii and Rosenthal. The proof relies on showing that a finitely generated group that is minor excluded with respect to every finite generating set is accessible, using a graph-theoretic characterisation of accessibility due to Thomassen and Woess.
