A Note on Large Characteristic Subgroups. Issue 11 (2nd November 2018) - de Giovanni, Francesco; Trombetti, Marco
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.