A generalization of 2-Baer groups.

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 generalizedT2-group. In particular, we provide structure results for such groups, investigate their nilpotency class, and construct examples of finitep-groups which are generalizedT2-groups. [ABSTRACT FROM AUTHOR]