Suppose we have a group with presentation G = <A|R> i.e G is the quotient of the free group F(A) on A by the normal closure <<A>> of some subset A of F(A). Is it true that that fundamental group of the Cayley graph of G (with respect to the generating set A) will be isomorphic to the subgroup <<A>> in F(A)? It seems to me that this should be true (and it agrees with the facts that: a subgroup of a free group is free and the fundamental group of a graph is free) but I can't find this theorem stated anywhere....(adsbygoogle = window.adsbygoogle || []).push({});

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Fundamental Group of a Cayley Graph

Loading...

Similar Threads - Fundamental Group Cayley | Date |
---|---|

A Fundamental group of a sphere with 6 points removed | Oct 15, 2017 |

A Fundamental group of n connect tori with one point removed | Oct 13, 2017 |

A Fundamental group of Project Plane with 2 points missing | Oct 12, 2017 |

I Homotopy Class vs Fundamental Group. | Sep 21, 2017 |

A Fundamental and Homology groups of Polygons | Dec 13, 2016 |

**Physics Forums - The Fusion of Science and Community**