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2023•Communications in AlgebraRequires access

The cyclic sequences in non-Abelian groups

Ömür Deveci, Anthony G. Shannon, Aytakın Mansımova

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Abstract

In this paper, we describe the cyclic 3-nacci sequence and the cyclic generalized order-3 Pell sequence in the non-abelian groups and then we investigate them in non-abelian finite groups in detail. Furthermore, we give the lengths of the periods of the cyclic 3-nacci sequence and the cyclic generalized order-3 Pell sequence in the polyhedral group (n,2,2) with respect to the generating triple (a,b,c) as applications of the results produced.

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What this paper is about

In this paper, we describe the cyclic 3-nacci sequence and the cyclic generalized order-3 Pell sequence in the non-abelian groups and then we investigate them in non-abelian finite groups in detail. Furthermore, we give the lengths of the periods of the cyclic 3-nacci sequence and the cyclic generalized order-3 Pell sequence in the polyhedral group (n,2,2) with respect to the generating triple (a,b,c) as applications of the results produced.

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Available abstract

In this paper, we describe the cyclic 3-nacci sequence and the cyclic generalized order-3 Pell sequence in the non-abelian groups and then we investigate them in non-abelian finite groups in detail. Furthermore, we give the lengths of the periods of the cyclic 3-nacci sequence and the cyclic generalized order-3 Pell sequence in the polyhedral group (n,2,2) with respect to the generating triple (a,b,c) as applications of the results produced.

Key concepts: Cyclic group, Abelian group, Mathematics, Sequence (biology), Order (exchange), Elementary abelian group, Combinatorics, Exact sequence

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