Automorphism groups of nilpotent groups

摘要

We construct a full class of nilpotent groups of class 2 of an arbitrary infinite cardinality κ. Their centers, commutator subgroups and factors modulo the center will be the same and a homogeneous direct sum of a group of rank 1 or 2. Their automorphism groups will coincide and the factor group modulo the stabilizer could be an arbitrary group of size ≦ κ.