THE FIRST FUNDAMENTAL GROUP OF THE PERMUTATION GROUP
DOI:
https://doi.org/10.25077/jmua.15.4.460-465.2026Keywords:
Identity graph, Permutation group, The first fundamental groupAbstract
This study aims to determine the elements of the first fundamental group based on identity graphs derived from permutation groups, particularly those representing symmetric groups. Identity graphs are constructed by treating vertices as group elements and connecting them with edges when their product results in the identity element. The research focuses on identifying the components of the first fundamental group within these graph structures. The elements of the fundamental group are interpreted as sets of equivalent closed paths that start and finish at the same vertex. The findings indicate that the number of these equivalence classes in a fundamental group constructed from an identity graph reflects specific graph structures, offering new perspectives on the connection between permutation groups and graph theory.
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