On Commutativity and Finiteness in Groups

2007/11/29 by Ricardo N. Oliveira, Oliveira, Ricardo N., Said N. Sidki +1
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems #math.GR

paper · pdf · doi:10.48550/arxiv.0711.4627

22 pages

openalex publication_date 2007/11/29 · arxiv created 2009/06/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The second author introduced notions of weak permutability and commutativity between groups and proved the finiteness of a group generated by two weakly permutable finite groups. Two groups H,K weakly commute provided there exists a bijection f: H -> K which fixes the identity element and such that h commutes with its image h^f for all h in H. The present paper gives support to conjectures about the nilpotency of groups generated by two weakly commuting finite abelian groups H,K.

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