On Commutativity and Finiteness in Groups

Details On Commutativity and Finiteness in Groups On Commutativity and Finiteness in Groups

2007-11-29

arxiv.org/abs/0711.4627v3

Mathematics

Group Theory

22 pages

Scientific paper

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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