Mathematical Sciences: Infinite Periodic Groups

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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.