Divisibility relation between the number of certain surjective group and ring homomorphisms

2025/02/20 by Kumar, Sonu, Mandal, Priyabrata
#11A41 #2000: 20K01 #20K30 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2502.14266

Abstract

In this article, we identify the existence of a divisibility relationship between the number of ring homomorphisms and surjective group homomorphisms. We demonstrate that for finite cyclic structures, the number of ring homomorphisms from ℤ_m to ℤ_n is a divisor of the number of surjective group homomorphisms from ℤ_m to ℤ_n, where n is not of the form 2 ⋅ α, where each prime factor p of α satisfies p ≡ 3 \pmod4. We further extend this result for finite abelian structures.

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