A generalization of 2-Baer groups

ABSTRACT

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 T₂-group. In particular, we provide structure results for such groups, investigate their nilpotency class, and construct examples of finite p-groups which are generalized T₂-groups.

KEYWORDS:

• 2-Baer group
• Engel element
• subnormal subgroup

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 20E15
• 20F19
• 20F45