Large Characteristic Subgroups with Restricted Conjugacy Classes
| Autor: | Francesco de Giovanni, Marco Trombetti |
|---|---|
| Přispěvatelé: | de Giovanni, F., Trombetti, M. |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: | |
| Popis: | It is well-known that every virtually abelian group contains an abelian characteristic subgroup of finite index. We shall say that a group class $$\mathfrak {X}$$ is F-characteristic if any group containing an $$\mathfrak {X}$$-subgroup of finite index has also a characteristic subgroup of finite index that belongs to $$\mathfrak {X}$$. Thus the class $$\mathfrak {A}$$ of abelian groups is F-characteristic. The aim of this paper is to prove that many interesting classes of infinite groups are F-characteristic. Moreover, it is shown that the class of free groups and that of free abelian groups are not F-characteristic. |
| Databáze: | OpenAIRE |
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