English

Nilpotent Groups are Round

Group Theory 2009-11-12 v1 Dynamical Systems

Abstract

We define a notion of roundness for finite groups. Roughly speaking, a group is round if one can order its elements in a cycle in such a way that some natural summation operators map this cycle into new cycles containing all the elements of the group. Our main result is that this combinatorial property is equivalent to nilpotence.

Keywords

Cite

@article{arxiv.0911.2048,
  title  = {Nilpotent Groups are Round},
  author = {D. Berend and M. D. Boshernitzan},
  journal= {arXiv preprint arXiv:0911.2048},
  year   = {2009}
}

Comments

11 pages

R2 v1 2026-06-21T14:10:02.623Z