International Postdoctoral Fellows Program: Rewriting Systems for Groups

该奖项隶属于国际博士后研究员计划，该计划使美国科学家和工程师能够在国外公认的卓越中心进行三到十二个月的研究。该计划的奖励为联合研究提供了机会，并利用独特或互补的设施、专业知识和国外的实验条件。该奖项将支持新墨西哥州立大学的Susan Hermiller博士对澳大利亚维多利亚墨尔本大学进行为期12个月的博士后研究访问，与John R. J. Groves博士合作。一组有限完全改写系统是一种以一种特别容易在计算机上实现的方式为组解决单词问题的表示，它提供了一种标准形式的规则语言。所提出的研究是对具有这种重写系统的一类群体的研究。将探讨几个问题。第一个问题：给定一个有有限完全重写系统的群，是否每个有限索引子群都有一个完整重写系统？第二，一个自动组是否一定有一个有限的完整的重写系统？第三-如果有限呈现群具有有限派生类型，它是否具有有限完全改写系统？为了回答这些问题，在可能的情况下，为更多的群体，特别是Artin群体构建重写系统是有帮助的。他们还打算研究由正规形式的子词闭正则语言给出的群的一个较弱的性质。该奖项建议提供资金用于支付国际旅行和12个月的津贴。

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.