Generating mapping class groups with elements of fixed finite order

Justin Lanier

Generating mapping class groups with elements of fixed finite order

Geometric Topology 2017-10-16 v1 Group Theory

Authors: Justin Lanier

Abstract

We show that for any $k$ at least $6$ and $g$ sufficiently large, the mapping class group of a surface of genus $g$ can be generated by three elements of order $k$ . We also show that this can be done with four elements of order $5$ . We additionally prove similar results for some permutation groups, linear groups, and automorphism groups of free groups.

Keywords

mapping class groups of surfaces mapping class groups finite groups

Cite

@article{arxiv.1710.04680,
  title  = {Generating mapping class groups with elements of fixed finite order},
  author = {Justin Lanier},
  journal= {arXiv preprint arXiv:1710.04680},
  year   = {2017}
}

Comments

24 pages, 11 figures

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