Gilbert Baumslag, City College of New York

Abstract:Many years ago Bernhard Neumann proved that every group can be embedded in a divisible group. Divisible groups can be viewed as exponential groups, i.e., groups which admit exponentiation by elements of a ring, i.e., groups with operators where the set of operators form a ring and satisfy some additional conditions. Such exponential groups include groups in which extraction of roots is uniquely possible and the groups with parametric exponents as defined by Roger Lyndon. I will discuss these and related groups and some of the open problems associated with them.