Mohammad Javaheri

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math.GR2025

R-harmonious groups

Mohammad Javaheri

A group is R-harmonious if there exists a permutation $g_{1}, g_{2}, \dots, g_{n - 1}$ of the non-identity elements of $G$ such that the consecutive products $g_{1} g_{2}$ , $g_{2} g_{3}$ , $\ldots,…

math.GR2025

Symmetric harmoniousness of odd-order groups

Mohammad Javaheri

We prove that every odd-order group is symmetric harmonious: there exists a permutation $g_{0}, g_{1}, \dots, g_{ℓ - 1}$ of elements of $G$ such that the consecutive products $g_0g_1,g…