The stable torsion length in a group is the stable word length with respect to the set of all torsion elements. We show that the stable torsion length vanishes in crystallographic groups. We then give a linear programming algorithm to compute a lower bound for stable torsion length in free products of groups. Moreover, we obtain an algorithm that exactly computes stable torsion length in free products of finite groups. The nature of the algorithm shows that stable torsion length is rational in this case. As applications, we give the 1st exact computations of stable torsion length for nontrivial examples.

中文翻译：

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稳定扭转长度

组中的稳定扭转长度是相对于所有扭转元素的集合的稳定字长。我们表明稳定的扭转长度在晶体组中消失。然后我们给出一个线性规划算法来计算组的自由乘积中稳定扭转长度的下限。此外，我们获得了一种算法，可以精确计算有限群的自由乘积中的稳定扭转长度。该算法的性质表明，在这种情况下，稳定的扭转长度是合理的。作为应用，我们给出了非平凡例子的稳定扭转长度的第一精确计算。