ON FINITE AND LOCALLY FINITE SUBGROUPS OF FREE BURNSIDE GROUPS OF LARGE EVEN EXPONENTS

The following basic results on infinite locally finite subgroups of a free m-generator Burnside group B(m, n) of even exponent n, where m > 1 and n greater than or equal to 2(48), n is divisible by 2(9), are ob tained: A clear complete description of all infinite groups that are e mbeddable in B(m, n) as (maximal) locally finite subgroups is given. A ny infinite locally finite subgroup L of B(m, n) is contained in a uni que maximal locally finite subgroup, while any finite a-subgroup of B( m, n) is contained in continuously many pairwise nonisomorphic maximal locally finite subgroups. In addition, L is locally conjugate to a ma ximal locally finite subgroup of B(m, n). To prove these and other res ults, centralizers of subgroups in B(m, n) are investigated. For examp le, it is proven that the centralizer of a finite 2-subgroup of B(m, n ) contains a subgroup isomorphic to a free Burnside group B(infinity,n ) of countably infinite rank and exponent n; the centralizer of a fini te non-a-subgroup of B(m, n) or the centralizer of a nonlocally finite subgroup of B(m, n) is always finite; the centralizer of a subgroup T is infinite if and only if T is a locally finite 2-group. (C) 1997 Ac ademic Press.