Abstract
An automorphism \(\alpha\) of a group \(G\) is called a class preserving automorphism if \(\alpha(g)\) and \(g\) are conjugate in \(G\) for each \(g \in G\) . We prove that each class preserving automorphism of the following nilpotent groups of class 2 is inner:
(i) The direct product of a generalized extraspecial \(\mathbb{Z}\) -group and a free abelian group with finite rank.
(ii) An extension of \(\mathbb{Q}\) by a direct sum of finitely many copies of \(\mathbb{Q}\) , where \(\mathbb{Q}\) is the additive group of rational numbers.
(iii) An infinite Černikov \(p\) -group which is not abelian but each proper quotient group is abelian.
