On Finite and Locally Finite Subgroups of Free Burnside Groups of Large Even Exponents Original Research Article

The following basic results on infinite locally finite subgroups of a freem-generator Burnside groupB(m, n) of even exponentn, wherem > 1 andn ≥ 248,nis divisible by 29, are obtained: A clear complete description of all infinite groups that are embeddable inB(m, n) as (maximal) locally finite subgroups is given. Any infinite locally finite subgroup image ofB(m, n) is contained in a unique maximal locally finite subgroup, while any finite 2-subgroup ofB(m, n) is contained in continuously many pairwise nonisomorphic maximal locally finite subgroups. In addition, image is locally conjugate to a maximal locally finite subgroup ofB(m, n). To prove these and other results, centralizers of subgroups inB(m, n) are investigated. For example, it is proven that the centralizer of a finite 2-subgroup ofB(m, n) contains a subgroup isomorphic to a free Burnside groupB(∞, n) of countably infinite rank and exponentn; the centralizer of a finite non-2-subgroup ofB(m, n) or the centralizer of a nonlocally finite subgroup ofB(m, n) is always finite; the centralizer of a subgroup image is infinite if and only if image is a locally finite 2-group.