Tubular free by cyclic groups and the strongest Tits alternative
Tubular free by cyclic groups and the strongest Tits alternative
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管状自由循环群和最强的 Tits 替代品
DOI：
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发表时间：
2015
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影响因子：
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通讯作者：
J. Button
中科院分区：
文献类型：
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作者：
J. Button
利用Wise的公平集准则，我们证明了每个被循环群释放的管状物在CAT(0)立方复数上自由作用。我们还证明了这些群有一个满足最强Tits择优的有限指标子群，这意味着每个子群要么是非交换自由群，要么是挠自由交换群。具体地说，格尔斯滕群是第一个已知的实际上具有这种性质的群，但它实际上并不特殊，也不实质上是自由的。
We show, using Wise's equitable sets criterion, that every tubular free by cyclic group acts freely on a CAT(0) cube complex. We also show that these groups have a finite index subgroup satisfying the strongest Tits alternative, which means that every subgroup either surjects a non abelian free group or is torsion free abelian. In particular the Gersten group is the first known group virtually having this property but which is not virtually special nor virtually residually free.