# Talk:Automorphism

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WikiProject Mathematics (Rated Start-class, Mid-priority)

## 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

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## 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:

• 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)

## 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)