A Note on Large Characteristic Subgroups. Issue 11 (2nd November 2018)

• Record Type: Journal Article
• Authors: de Giovanni, Francesco; Trombetti, Marco
• Is Part Of: Communications in algebra. Volume 46:Issue 11(2018)
• Page Start: 4654
• Page End: 4662
• Publication Date: 2018-11-02
• Subjects: Abelian subgroup -- characteristic subgroup -- twin map; 20E07; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2018.1448851
• Languages: English
• ISSNs: 0092-7872

Abstract

ABSTRACT: It is known that if a group G has an abelian subgroup of finite index n, then it contains an abelian characteristic subgroup A of index at most n n . The aim of this paper is to improve this bound by showing that the characteristic subgroup A can be chosen of index at most n 2 . Examples prove that this bound is the best possible. Our main result is obtained as an application of a general method for the construction of large characteristic subgroups.