
TL;DR
This paper introduces R-harmonious groups, a class characterized by a special permutation property of their non-identity elements, and proves that all odd-order groups not divisible by 3 are R-harmonious.
Contribution
It defines R-harmonious groups and establishes a significant class of such groups, expanding understanding of their structural properties.
Findings
Every group of odd order not divisible by 3 is R-harmonious.
The study employs cyclic and split extensions to analyze R-harmonious groups.
Abstract
A group is R-harmonious if there exists a permutation of the non-identity elements of such that the consecutive products , , also form a permutation of the non-identity elements, where . We investigate R-harmonious groups via cyclic and split extensions. Among our results, we prove that every group of odd-order not divisible by 3 is R-harmonious.
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Taxonomy
TopicsFinite Group Theory Research · Advanced Combinatorial Mathematics · Quasicrystal Structures and Properties
