A generalization of 2-Baer groups. Issue 9 (2nd September 2017)

• Record Type: Journal Article
• Authors: Kappe, Luise-Charlotte; Tortora, Antonio
• Is Part Of: Communications in algebra. Volume 45:Issue 9(2017)
• Page Start: 3994
• Page End: 4001
• Publication Date: 2017-09-02
• Subjects: 2-Baer group -- Engel element -- subnormal subgroup; 20E15 -- 20F19 -- 20F45; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2016.1252385
• Languages: English
• ISSNs: 0092-7872

Abstract

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 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.