Some remarks on central automorphisms of hypercentral groups (Q1262394)

The authors examine the exponent of the group \(Aut_ c(G)\) of central automorphisms of a hypercentral group G. The paper contains results relating the exponents of the torsion part of a nilpotent group G and the torsion part of its centre and the exponents of \(Aut_ c(G)\) and other subgroups of Aut G. Amongst other results it is proved the existence of hypercentral groups with groups of central automorphisms of finite exponent, though their centre is of infinite exponent. The proofs are given with the aid of results of the cohomology theory.