$f$-REPRESENTATIVES GROUPS

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International Electronic Journal of Algebra
Volume:30 Issue:30
$f$-REPRESENTATIVES GROUPS

$f$-REPRESENTATIVES GROUPS

Pages : 66-77

View : 18 | Download : 18

Publication Date : 2021-07-17

Article Type : Research Paper

Abstract :The $b$-parts, $b$-addition of real numbers and some of their extensions insert ignore into journalissuearticles values(e.g., $f$-multiplications); were introduced and studied by the author. In this paper, we introduce $f$-representatives groups of a given group $insert ignore into journalissuearticles values(G,\cdot);$ which can be considered as a generalization of the group of the least non-negative residues insert ignore into journalissuearticles values(modulo $n$);. Thereafter, we study some of their important properties and their relations among the ground group $insert ignore into journalissuearticles values(G,\cdot);$, 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.
Keywords : b Addition, f multiplication, f grouplike, decomposer function

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