M.Sc Thesis | |

M.Sc Student | Reiter Asael |
---|---|

Subject | Randomly Generating the Symmetric Group, by Word Maps |

Department | Department of Mathematics |

Supervisors | ASSOCIATE PROF. Chen Meiri |

ASSOCIATE PROF. Danny Neftin | |

Full Thesis text |

It is known, for the past half century, that two random permutations
almost surely generate the symmetric group *S _{n}* or the
alternating group

In this work, we consider the images of random substitutions in a general set of word maps. Using Stallings core graphs, and some ideas from graph theory and combinatorics, we explain how it can be analyzed. The main result of this paper is that the generated group, in this setup, is almost surely transitive. This is an improvement of previous results, that had only shown that this group does not have any fixed point .

Our method can be slightly generalized. Unfortunately, this generalization
is not enough to show that the generated group is almost surely *A _{n}*
or