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Finite Groups of Uniform Logarithmic Diameter

群论 2007-05-23 v1

摘要

We give an example of an infinite family of finite groups GnG_n such that each GnG_n can be generated by 2 elements and the diameter of every Cayley graph of GnG_n is O(log(Gn))O(\log (| G_{n}|)). This answers a question of Lubotzky.

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引用

@article{arxiv.math/0506007,
  title  = {Finite Groups of Uniform Logarithmic Diameter},
  author = {Miklos Abert and Laszlo Babai},
  journal= {arXiv preprint arXiv:math/0506007},
  year   = {2007}
}