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arXiv · 0711.4627

On Commutativity and Finiteness in Groups

Ricardo N. Oliveira·Said N. Sidki
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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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Ricardo N. Oliveira, Said N. Sidki. 2009-06-28. On Commutativity and Finiteness in Groups. https://arxiv.org/abs/0711.4627

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