Star graphs, projective planes and free subgroups in small cancellation groups
Star graphs, projective planes and free subgroups in small cancellation groups
复制标题
小取消群中的星图、射影平面和自由子群
DOI：
10.1112/plms/s3-57.2.301
复制
发表时间：
1988
影响因子：
1.8
通讯作者：
J. Howie
中科院分区：
文献类型：
--
作者：
M. Edjvet;J. Howie
小消去群，如一个相关子群，是表面群的推广，满足与这些群相关的许多良好性质。本文讨论了允许2阶自由子群的性质。Collins[5]的一个结果断言，除了少数明显的例外，由满足C(4)和T(4)的表示所给出的群包含2阶自由子群。C(6)群的类似结果被Al-Janabi[1]证明(另见[2])。El-Mosalamy用星图证明了Collins的结果[7]。本文还利用星图，证明了满足(非度量)小消去条件C(3)和T(6)的第三个标准集的群的类似定理(定义见§2)。
Small cancellation groups, like one-relator groups, are generalizations of surface groups, and satisfy many of the nice properties associated with those groups. The present paper concerns the property of admitting a free subgroup of rank 2. A result of Collins [5] asserts that, with a few obvious exceptions, a group given by a presentation satisfying C (4) and T (4) contains a free subgroup of rank 2. The analogous result for C (6) groups was proved by Al-Janabi [1](see also [2]). An alternative proof of Collins's result, using star graphs, is given by El-Mosalamy [7]. In this paper we also use star graphs, and prove an analogous theorem for groups satisfying the third of the standard sets of (non-metric) small-cancellation conditions C (3) and T (6)(see § 2 for a definition).