Given an integer $n$, we denote by $mathfrak B_n$ and $mathfrak C_n$ the classes of all groups $G$ for which the map $phi_{n}:gmapsto g^n$ is a monomorphism and an epimorphism of $G$, respectively. In this paper we give a characterization for groups in $mathfrak B_n$ and for groups in $mathfrak C_n$. We also obtain an arithmetic description of the set of all integers $n$ such that a group $G$ is in $mathfrak B_ncapmathfrak C_n$.
Some special classes of n-abelian groups
DELIZIA, Costantino;TORTORA, ANTONIO
2012-01-01
Abstract
Given an integer $n$, we denote by $mathfrak B_n$ and $mathfrak C_n$ the classes of all groups $G$ for which the map $phi_{n}:gmapsto g^n$ is a monomorphism and an epimorphism of $G$, respectively. In this paper we give a characterization for groups in $mathfrak B_n$ and for groups in $mathfrak C_n$. We also obtain an arithmetic description of the set of all integers $n$ such that a group $G$ is in $mathfrak B_ncapmathfrak C_n$.File in questo prodotto:
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