$f$-REPRESENTATIVES GROUPS

Abstract

The $b$-parts, $b$-addition of real numbers and some of their extensions (e.g., $f$-multiplications) were introduced and studied by the author. In this paper, we introduce $f$-representatives groups of a given group $(G,\cdot)$ which can be considered as a generalization of the group of the least non-negative residues (modulo $n$). Thereafter, we study some of their important properties and their relations among the ground group $(G,\cdot)$, a related quotient group, and $f$-grouplikes. Finally, many equivalent conditions for $f$-representatives groups and several examples in the group of real numbers are given.