  A group in which all cyclic subgroups are 2-subnormal is called a 2-Baer
group. The topic of this paper are generalized 2-Baer groups, i.e. groups in
which the non-2-subnormal cyclic subgroups generate a proper subgroup of the
group. If this subgroup is non-trivial, the group is called a generalized
T_2-group. In particular, we provide structure results for such groups,
investigate their nilpotency class and construct examples of finite p-groups
which are generalized T_2-groups.
