当前位置: X-MOL 学术Int. J. Algebra Comput. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
The conjugacy problem for Higman’s group
International Journal of Algebra and Computation ( IF 0.5 ) Pub Date : 2020-06-22 , DOI: 10.1142/s0218196720500393
Owen Baker

Higman’s group [Formula: see text] is a remarkable group with large (non-elementary) Dehn function. Higman constructed the group in 1951 to produce the first examples of infinite simple groups. Using finite state automata, and studying fixed points of certain finite state transducers, we show the conjugacy problem in [Formula: see text] is decidable for all inputs. Diekert, Laun and Ushakov have recently shown the word problem in [Formula: see text] is solvable in polynomial time, using the power circuit technology of Myasnikov, Ushakov and Won. Building on this work, we also show in a strongly generic setting that the conjugacy problem for [Formula: see text] has a polynomial time solution.

中文翻译:

Higman 群的共轭问题

Higman 群 [公式:见正文] 是一个具有大(非初等)德恩函数的显着群。Higman 在 1951 年构建了该群,以产生第一个无限单群的例子。使用有限状态自动机,并研究某些有限状态换能器的不动点,我们展示了[公式:见文本]中的共轭问题对于所有输入都是可判定的。Diekert、Laun 和 Ushakov 最近使用 Myasnikov、Ushakov 和 Won 的电源电路技术证明了 [公式:见正文] 中的单词问题在多项式时间内是可解的。在这项工作的基础上,我们还在一个非常通用的设置中展示了 [公式:见文本] 的共轭问题具有多项式时间解。
更新日期:2020-06-22
down
wechat
bug