论文标题
在有限生成的正常亚组的右角Artin组和组的图形产品上
On finitely generated normal subgroups of right-angled Artin groups and graph products of groups
论文作者
论文摘要
Schreier指出的经典结果是，自由组的非平凡有限生成的正常亚组是有限索引，也就是说，自由组只能对具有有限生成的内核的有限基团宣传。 在本说明中，我们将此结果扩展到右角Artin组（RAAGS）的类别。更确切地说，我们证明有限生成的（完整）正常亚组的RAAG的商是逐句和有限的by-Abelian。 随着Schreier的结果扩展到群体的非平凡免费产品，我们进一步表明我们的结果扩展到了组的图形产品。 作为推论，我们推断出有限的RAAG的正常亚组具有可决定性的单词，共轭和会员问题，并且它们在遗传上是可分离的。
A classical result of Schreier states that nontrivial finitely generated normal subgroups of free groups are of finite index, that is, free groups can only quotient to finite groups with finitely generated kernel. In this note we extend this result to the class of right-angled Artin groups (RAAGs). More precisely, we prove that the quotient of a RAAG by a finitely generated (full) normal subgroup is abelian-by-finite and finite-by-abelian. As Schreier's result extends to nontrivial free products of groups, we further show that our result extends to graph products of groups. As a corollary, we deduce, among others, that finitely generated normal subgroups of RAAGs have decidable word, conjugacy and membership problems and that they are hereditarily conjugacy separable.
