A minimal non-solvable group of homeomorphisms
A minimal non-solvable group of homeomorphisms
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同胚的最小不可解群
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
C. Bleak
中科院分区：
文献类型：
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作者：
C. Bleak
设PLoI表示单位区间的保定向分段线性同态群，在合成运算下，它允许有限多个斜率中断。我们找到了一个不可解群W，并证明了W嵌入到PLoI/的每个不可解子群中。我们发现在温和的条件下，其它不可解子群B，.O Zo/1、.Zo/1和1。O Z/)嵌入到PLoI/的子群中。证明了PLoI/的所有可解子群嵌入到PLoI/的所有非可解子群中。如果我们用任何广义Thompson群F_n来代替PLoI_i/，这些结果仍然适用。
Let PLo.I/ represent the group of orientation-preserving piecewise-linear homeo- morphisms of the unit interval which admit finitely many breaks in slope, under the operation of composition. We find a non-solvable groupW and show thatW embeds in every non-solvable subgroup of PLo.I/. We find mild conditions under which other non-solvable subgroups B, . o Z o/ 1 ,.Z o/ 1 , and 1 . o Z/) embed in subgroups of PLo.I/. We show that all solvable subgroups of PLo.I/ embed in all non-solvable subgroups of PLo.I/. These results continue to apply if we replace PLo.I/ by any generalized Thompson groupFn.