International Postdoctoral Fellows Program: Rewriting Systems for Groups

该奖项是根据国际 博士后研究员计划，使 美国科学家和工程师将进行三次 在国外中心进行为期12个月的研究 证明卓越。 该计划的奖项 提供联合研究的机会， 使用独特或互补的设施， 国外的实验条件和经验。 该奖项将支持为期12个月的 苏珊博士的博士后研究访问 新墨西哥州州立大学的赫米勒 澳大利亚维多利亚墨尔本大学， 与约翰·R博士一起工作格罗夫斯。 群的有限完全重写系统 是一个解决单词问题的演示 以一种特别 容易在计算机上实现， 提供了正规形式的正则语言。 这项研究是对这一班学生的一项研究 拥有这种重写系统的群体。 几 问题将继续下去。 第一个-给定 具有有限完全重写系统的群， 是否每个有限指数子群也都有一个？ 第二个-自动组 一定有一个有限的完全重写 系统？ 第三种-如果一个人提出 群有有限导子型，是否有 有限完全重写系统 回答 这些问题，将有助于 为更多家庭构建重写系统 特别是Artin群，如果 可能 他们还打算研究一种较弱的 由闭子字给出的群的属性 正规形式的正规语言。 授标建议提供资金， 包括国际旅行和津贴 十二个月。

This award is under the International Postdoctoral Fellows Program, which enables U.S. scientists and engineers to conduct three to twelve months of research at foreign centers of proven excellence. The program's awards provide opportunities for joint research, and the use of unique or complementary facilities, expertise and experimental conditions abroad. This award will support a twelve-month postdoctoral research visit by Dr. Susan Hermiller of New Mexico State University to the University of Melbourne, Victoria, Australia, to work with Dr. John R. J. Groves. A finite complete rewriting system for a group is a presentation which solves the word problem for the group in a way that is particularly easy to implement on a computer, and which provides a regular language of normal forms. The proposed research is a study of the class of groups with such rewriting systems. Several questions will be pursued. The first - Given a group with a finite complete rewriting system, must every finite index subgroup also have one? The second - Does an automatic group necessarily have a finite complete rewriting system? The third - If a finitely presented group has finite derivation type, does it have a finite complete rewriting system? To answer these questions, it would be helpful to construct rewriting systems for more families of groups, especially Artin groups, if possible. They also intend to study a weaker property for a group, given by a subword closed regular language of normal forms. The award recommendation provides funds to cover international travel and a stipend for twelve months.