Graf Konjugasi dari Hasil Kali Langsung Grup Alternating A4 dan Grup Simetri S3

Muhammad Fikri Muammar; Ahmad Faisol; Fitriani Fitriani

doi:10.37905/jjom.v7i2.32926

Graf Konjugasi dari Hasil Kali Langsung Grup Alternating A4 dan Grup Simetri S3

Muhammad Fikri Muammar, Ahmad Faisol, Fitriani Fitriani

Abstract

This study investigates the structure of conjugacy graphs formed from the conjugacy classes in the alternating group A4, the symmetric group S3, and their direct product A4 × S3. Using Mathematica, the conjugacy classes of each group are determined, and the corresponding conjugacy graphs are constructed to represent the relationships between the classes. The results show that the conjugacy graphs of A4 × S3 form a complete graph Kᵢ×ⱼ, where i and j are the number of conjugacy classes in A4 and S3, respectively. These findings indicate that the conjugacy structure of the direct product exhibits a distinctive combinatorial complexity derived from its component groups.

Keywords

Conjugacy Classes; Symmetric Groups; Alternating Groups; Conjugacy Graphs

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DOI: https://doi.org/10.37905/jjom.v7i2.32926