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- In [[algebra]], an '''automorphism''' of an [[abstract algebra]]ic structure is an [[isomorphism]] of the stru The automorphisms typically form a [[group theory|group]], the '''automorphism group''' of the structure.368 bytes (48 words) - 07:49, 5 February 2009
- #REDIRECT [[Conjugation (group theory)#Inner automorphism]]59 bytes (6 words) - 14:26, 15 November 2008
- #REDIRECT [[Frobenius map#Frobenius automorphism]]50 bytes (5 words) - 15:38, 7 December 2008
- 166 bytes (22 words) - 22:30, 7 February 2009
- In [[field theory]], a '''field automorphism''' is an [[automorphism]] of the [[algebraic structure]] of a [[field (mathematics)|field]], that i ...phisms of a given field ''K'' form a [[group (mathematics)|group]], the '''automorphism group''' <math>Aut(K)</math>.3 KB (418 words) - 12:18, 20 December 2008
- 151 bytes (20 words) - 16:36, 20 November 2008
- 688 bytes (93 words) - 12:57, 21 November 2008
- Auto-populated based on [[Special:WhatLinksHere/Automorphism]]. Needs checking by a human. {{r|Field automorphism}}525 bytes (65 words) - 11:10, 11 January 2010
- 866 bytes (139 words) - 16:35, 20 November 2008
Page text matches
- In [[field theory]], a '''field automorphism''' is an [[automorphism]] of the [[algebraic structure]] of a [[field (mathematics)|field]], that i ...phisms of a given field ''K'' form a [[group (mathematics)|group]], the '''automorphism group''' <math>Aut(K)</math>.3 KB (418 words) - 12:18, 20 December 2008
- #REDIRECT [[Conjugation (group theory)#Inner automorphism]]59 bytes (6 words) - 14:26, 15 November 2008
- In [[algebra]], an '''automorphism''' of an [[abstract algebra]]ic structure is an [[isomorphism]] of the stru The automorphisms typically form a [[group theory|group]], the '''automorphism group''' of the structure.368 bytes (48 words) - 07:49, 5 February 2009
- A subgroup which is mapped to itself by any automorphism of the whole group.112 bytes (17 words) - 16:19, 6 November 2008
- ==Frobenius automorphism== When ''F'' is surjective as well as injective, it is called the '''Frobenius automorphism'''. One important instance is when the domain is a [[finite field]].1 KB (166 words) - 18:17, 16 February 2009
- ==Inner automorphism== ...T_{y^{-1}}</math>, it is an [[automorphism]] of ''G'', termed an '''inner automorphism'''. The inner automorphisms of ''G'' form a group <math>Inn(G)</math> and2 KB (294 words) - 04:53, 19 November 2008
- Auto-populated based on [[Special:WhatLinksHere/Automorphism]]. Needs checking by a human. {{r|Field automorphism}}525 bytes (65 words) - 11:10, 11 January 2010
- #REDIRECT [[Frobenius map#Frobenius automorphism]]50 bytes (5 words) - 15:38, 7 December 2008
- ...t defined over a finite field which has successive powers of the Frobenius automorphism applied to the first column.164 bytes (23 words) - 15:53, 28 October 2008
- ...' if it mapped to itself by any [[group automorphism]], that is: given any automorphism <math>\sigma</math> of ''G'' and any element ''h'' in ''H'', <math>\sigma(h ...s the intersection of all maximal subgroups, is characteristic because any automorphism will take a maximal subgroup to a maximal subgroup.2 KB (358 words) - 02:37, 18 November 2008
- ...omplex numbers over the field of real numbers, and is the only non-trivial automorphism. One can say it is impossible to tell which is ''i'' and which is -''i''.906 bytes (139 words) - 13:16, 20 November 2008
- ...of characteristic ''p''. The [[Frobenius map]] is an [[field automorphism|automorphism]] of ''F'' and so its [[inverse function|inverse]], the ''p''-th root map i2 KB (295 words) - 15:43, 7 December 2008
- # Every [[inner automorphism]] of ''G'' sends ''H'' to within itself # Every [[inner automorphism]] of ''G'' restricts to an automorphism of ''H''5 KB (785 words) - 09:22, 30 July 2009
- {{r|Field automorphism}}522 bytes (67 words) - 20:03, 11 January 2010
- ...e prime ideal <math> \mathfrak{P} </math>. Also, although the [[Frobenius automorphism]] is only determined up to an element of <math> I_{\mathfrak{P}} </math>, t2 KB (315 words) - 15:49, 10 December 2008
- {{r|Field automorphism}}594 bytes (76 words) - 19:15, 11 January 2010
- {{r|Field automorphism}}530 bytes (68 words) - 19:04, 11 January 2010
- {{r|Field automorphism}}692 bytes (91 words) - 16:33, 11 January 2010
- {{r|Field automorphism}}710 bytes (90 words) - 19:54, 11 January 2010
- {{r|Automorphism}}656 bytes (94 words) - 12:34, 8 November 2008
- {{r|Field automorphism}}644 bytes (86 words) - 19:50, 11 January 2010
- ...ernel]] of the [[group homomorphism|homomorphism]] to ''G'' to its [[inner automorphism]] group.785 bytes (114 words) - 11:29, 13 February 2009
- {{r|Field automorphism}}857 bytes (112 words) - 16:32, 11 January 2010
- {{r|Field automorphism}}873 bytes (139 words) - 12:36, 20 November 2008
- {{r|Field automorphism}}1 KB (146 words) - 16:32, 11 January 2010
- {{r|Field automorphism}}990 bytes (154 words) - 13:18, 20 December 2008
- {{r|Field automorphism}}1 KB (169 words) - 08:53, 22 December 2008
- {{r|Field automorphism}}1 KB (169 words) - 19:54, 11 January 2010
- {{r|Automorphism}}1 KB (180 words) - 17:00, 11 January 2010
- {{r|Field automorphism}}1 KB (187 words) - 20:18, 11 January 2010
- ...p]] is cyclic of order two, with the non-trivial element being the [[field automorphism]] If ''F'' is a complex quadratic field then this automorphism is induced by [[complex conjugation]].3 KB (453 words) - 17:18, 6 February 2009
- ...ath)|matrix]]'''. A Moore matrix has successive powers of the [[Frobenius automorphism]] applied to the first column, i.e., an ''m'' × ''n'' matrix1 KB (199 words) - 15:30, 7 December 2008
- {{r|Automorphism}}2 KB (247 words) - 06:00, 7 November 2010
- *a group containing all [[field automorphism]]s in ''L'' that leave the elements in ''K'' untouched - the Galois group o ...y 2 automorphisms of L that leave every element of Q alone: the do-nothing automorphism <math>\phi_0: a+b r_0 \rightarrow a + b r_0 </math> and the map <math>\ph4 KB (683 words) - 22:17, 7 February 2010
- ...oup is, in general, difficult. Because abelian groups have a trivial inner automorphism subgroup, finding automorphisms for abelian groups is, strangely enough, ha15 KB (2,535 words) - 20:29, 14 February 2010
- ...s therefore also [[surjective function|surjective]] (it is the [[Frobenius automorphism]]). Suppose that ''F'' is finite, of characteristic two. The Frobenius map is an automorphism and so its [[inverse function|inverse]], the square root map is defined eve10 KB (1,580 words) - 08:52, 4 March 2009
- * The [[automorphism group]] of an algebraic structure acts on the structure.4 KB (727 words) - 12:37, 16 November 2008
- ...e sense that every point can be transformed into every other point by some automorphism.28 KB (4,311 words) - 08:36, 14 October 2010