Talk:Automorphism

Olivier/Millar

(I am not satisfied with that, it is too much jargon, there should be an example, it does not convey the power of the concept and is just a definition) -- Olivier.

Not only that, but what the heck is it?!?! Seriously, I think good encyclopedia articles should assume that the reader may not know the context of the article.

A single introductory sentence describing the context can make all the difference in the world. -- Alan Millar

Link suggestions

An automated Wikipedia link suggester has some possible wiki link suggestions for the Automorphism article, and they have been placed on this page for your convenience.
Tip: Some people find it helpful if these suggestions are shown on this talk page, rather than on another page. To do this, just add {{User:LinkBot/suggestions/Automorphism}} to this page. — LinkBot 01:01, 18 Dec 2004 (UTC)

I added the links that made sense. Edward 07:52, 22 Dec 2004 (UTC)

Centerless?

It talks of "if G is centerless" in the examples, but isn't G a group, and so contains the identity, which is commutative by definition, and hence all centers contain the identity? so doesn't this put the talk of a centerless group as impossible? -- Moxmalin

By definition, a group is centerless if its center consists of only the identity. See center of a group. -- Fropuff 00:16, 9 February 2007 (UTC)[reply]

Automorphisms of R

Currently the article states that R has no non-trivial order-preserving field-automorphisms, which is true, but potentially misleading since in fact R has no non-trivial field-automorphisms at all (since the order can be recovered from the field operations, as the positive elements are precisely the nonzero squares). I'm changing it. Algebraist 17:15, 22 March 2008 (UTC)[reply]

Not maps

The following examples were removed:

In puzzles, automorphism exists when elements of the puzzle have a type of symmetry among the elements and their positions, such as an automorphic Sudoku.
An example of an automorphism is a similarity transform, which leaves the geometrical form of a figure unchanged.<ref Klaus Maintzer: Local activity principle: The cause of complexity and symmetry breaking, Chapter 12 (pages 146–159). In: {{cite book|author1=Andrew Adamatzky|author2=Guanrong Chen|title=Chaos, CNN, Memristors and Beyond: A Festschrift for Leon ChuaWith DVD-ROM, composed by Eleonora Bilotta|url=https://books.google.com/books?id=Tve6CgAAQBAJ&pg=PA149%7Cdate=2 January 2013|publisher=World Scientific|isbn=978-981-4434-81-2|pages=149–150}} ref>

This article refers to a certain class of self-mappings of a mathematical object. The Sudoku section corresponds in title but not content to this article. The Similarity redlink and Maintzer ref are inappropriate for this article. — Rgdboer (talk) 00:51, 7 January 2018 (UTC)[reply]

Inconsistencies with General linear group

The linear algebra example states: "When the vector space is finite-dimensional, the automorphism group of V is the same as the general linear group, GL(V)."

This suggests that this is not the case for infinite-dimensional vector spaces. However, the article on the General linear group states that GL(V) = Aut(V) in general: "V is a vector space over the field F, the general linear group of V, written GL(V) or Aut(V), is the group of all automorphisms of V, [...]. If V has finite dimension n, then GL(V) and GL(n, F) are isomorphic." — Preceding unsigned comment added by 149.172.82.115 (talk) 15:45, 11 June 2019 (UTC)[reply]