Mathematical Sciences: Infinite Periodic Groups

为了得到自由Burnside群的有限子群在次指数时间内的完全刻画；研究自由Burnside群的标准表示的次表示的各种性质和这些群的分裂自同构；构造无限单2-群和2-生成的有界指数的无限2-群的显式例子，主要研究者将进一步发展最近建立的机制来解决偶数指数周期群中的Burnside问题，以获得自由Burnside群的有限子群的完全刻画；研究自由Burnside群的标准表示的次表示的各种性质以及这些群的分裂自同构的各种性质；群是定义了乘法的代数对象。群可以有无限个元素，也可以有有限个元素。最近，这位研究人员为偶数指数提供了著名的Burnside问题的解决方案，这是一个自世纪之交以来一直悬而未决的问题。该奖项支持为解决这一问题而开发的技术的努力。这项工作与数学的几个领域以及计算机科学都有联系。

The principal investigator will further develop the machinery recently created to solve the Burnside problem in periodic groups for even exponents greater than 1 in order to obtain a complete description of finite subgroups of free Burnside groups; to solve the word problem for free Burnside groups in subexponential time; to investigate various properties of subpresentations of standard presentations of free Burnside groups and splitting automorphisms of these groups; to construct explicit examples of infinite simple 2-groups and 2-generated infinite 2-groups of bounded exponent all of whose proper subgroups are locally finite. A group is an algebraic object having a multiplication defined on it. Groups can have an infinite number of elements or a finite number of elements. Recently, this researcher has provided a solution to the famous Burnside problem for even exponents, a problem which has been open since the turn of the century. This award supports an effort to exploit the techniques developed for the solution of this problem. The work has connections to several areas of mathematics, as well as computer science.