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
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 * 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)

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)

Not maps
The following examples were removed: 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)
 * 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.

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)