Struktur Grup pada Pocket Cube

Abstract

The objective of this research is to examine the abstraction of a semi-direct product group that originates from a specific object, which is the pocket cube. The process involves constructing groups by identifying free groups that are produced from reduced rotation sequences with finite standard rotations within the pocket cube. Moreover, by taking the action group to the position and orientation of the cubino on the pocket cube, the set of member pairs in S_8 and Z_3^8 is derived. The investigation then focuses on various valid random patterns on the pocket cube to determine how they correspond to each element in the semi-direct product of S_8 and Z_3^8. Additionally, the study describes the randomness of the pocket cube pattern when two reduced rotation sequences are applied sequentially by analyzing the operational representation of the semi-direct product group members.Keywords: group, pocket cube, semi-direct product.