AI 中文总结
研究由图形小消去表示定义的群，证明C(4)-T(4)表示定义的群的挠子群有限，在特定假设下C(6)表示定义的群也如此，通过关于挠群作用在单连通图形小消去复形上的局部到全局不动点性质得出结论。
AI 中文摘要
图形小消去扩展了经典小消去理论，为在凯莱图中构造具有规定子图的群提供了有力方法。我们证明了由可能无限的C(4)-T(4)图形小消去表示定义的群的挠子群是有限的。在表示是无挠本质C(6)自由的附加假设下，我们也证明了由C(6)图形小消去表示定义的群的相应结果。这两个结果都来自于关于挠群通过自同构作用在单连通图形小消去复形上的局部到全局不动点性质的更一般结果。
英文摘要
Graphical small cancellation extends the classical small cancellation theory and provides a powerful method for constructing groups with prescribed subgraphs in their Cayley graphs. We prove that torsion subgroups of groups defined by possibly infinite C(4)-T(4) graphical small cancellation presentations are finite. We also prove the corresponding result for groups defined by C(6) graphical small cancellation presentations under the additional assumption that the presentation is torsion-essentially C(6)-free. Both results follow from a more general result on local-to-global fixed point properties for torsion groups acting by automorphisms on simply connected graphical small cancellation complexes.
Comments31 pages, 16 figures. Comments welcome
