Mathematical Sciences: Infinite Periodic Groups

首席研究员将进一步发展最近建立的机器，以解决周期群中的伯恩赛德问题，甚至指数大于1，以获得自由伯恩赛德群的有限子群的完整描述;解决自由伯恩赛德群在次指数时间的文字问题;研究自由伯恩赛德群的标准表示的子表示的各种性质和这些群的分裂自同构;构造了真子群局部有限的无限单2-群和2-生成的有界指数无限2-群的显式例子。 一个群是一个代数对象，在它上面定义了乘法。群可以有无限个元素，也可以有有限个元素。 最近，这位研究者提供了一个解决方案，著名的伯恩赛德问题，甚至指数，一个问题，一直开放以来的世纪之交。 该奖项支持努力利用为解决这一问题而开发的技术。 这项工作与数学的几个领域以及计算机科学有关。

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.