A Note on Large Characteristic Subgroups |
| |
Authors: | Francesco de Giovanni Marco Trombetti |
| |
Institution: | Dipartimento di Matematica e Applicazioni, Universitá di Napoli Federico II, Napoli, Italy |
| |
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 nn. The aim of this paper is to improve this bound by showing that the characteristic subgroup A can be chosen of index at most n2. 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. |
| |
Keywords: | Abelian subgroup characteristic subgroup twin map |
|