Characteristics of the Structure of Abelian Groups of Order (p^n) via Invariant Factors and Elementary Divisors
DOI:
https://doi.org/10.24252/msa.v14i2.70159Keywords:
Finite Abelian Group, Order (p^n ), Invariant Factor, Elementary Divisor, Fundamental TheoremAbstract
Finite Abelian groups are one of the key objects in abstract algebra as their structure can be completely classified via the Fundamental Theorem of Finite Abelian Groups. This study aims to describe the classification of finite Abelian groups of order (pn ), explain the relationship between invariant factors and elementary divisors, and demonstrate the structural characteristics of the groups based on integer partitions. The research method employed was qualitative research using a literature review and theoretical analysis. The results show that every finite Abelian group of order (pn ) can be expressed as the direct product of cyclic groups of prime powers. The invariant factor form provides a hierarchical representation based on divisibility properties, whilst the elementary divisor form provides a representation based on elementary prime factors. The number of non-isomorphic Abelian groups of order (pn ) is equal to the number of partitions of (n).
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