Talk:Automorphism
WikiProject Mathematics  (Rated Startclass, Midpriority)  


Olivier/Millar[edit]
(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
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 I added the links that made sense. Edward 07:52, 22 Dec 2004 (UTC)
Centerless?[edit]
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[edit]
Currently the article states that R has no nontrivial orderpreserving fieldautomorphisms, which is true, but potentially misleading since in fact R has no nontrivial fieldautomorphisms 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[edit]
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 bookauthor1=Andrew Adamatzkyauthor2=Guanrong Chentitle=Chaos, CNN, Memristors and Beyond: A Festschrift for Leon ChuaWith DVDROM, composed by Eleonora Bilottaurl=https://books.google.com/books?id=Tve6CgAAQBAJ&pg=PA149%7Cdate=2 January 2013publisher=World Scientificisbn=9789814434812pages=149–150}} ref>
This article refers to a certain class of selfmappings 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)
Inconsistencies with General linear group[edit]
The linear algebra example states: "When the vector space is finitedimensional, the automorphism group of V is the same as the general linear group, GL(V)."
This suggests that this is not the case for infinitedimensional 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)