I have a question about Automorphisms. Please check the following statement for validity....(adsbygoogle = window.adsbygoogle || []).push({});

An automorphism of a group should map generators to generators. Suppose it didn't, well then the group structure wouldn't be preserved and since automorphisms are homomorphisms this would be a contradiction.

If this is valid is there an example of a homomorphism (not an automorphism) of groups, say ##\phi:G\to H## that doesn't map a generator of ##G## to a generator of ##H##?

**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!

# Abstract Algebra: Automorphisms

Tags:

Loading...

Similar Threads - Abstract Algebra Automorphisms | Date |
---|---|

I What are the groups for NxNxN puzzle cubes called? | Dec 24, 2017 |

I Free Groups | Oct 19, 2017 |

B What do "linear" and "abstract" stand for? | Jun 7, 2017 |

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