  The article deals with profinite groups in which the centralizers are abelian
(CA-groups), that is, with profinite commutativity-transitive groups. It is
shown that such groups are virtually pronilpotent. More precisely, let G be a
profinite CA-group. It is shown that G has a normal open subgroup N which is
either abelian or pro-p. Further, a rather detailed information about the
finite quotient G/N is obtained.
