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- ...or '''normal divisor''', is a (proper or improper) subgroup ''H'' of the [[group]] ''G'' that is invariant under [[conjugation]] by all elements of ''G''. ...at: ''g h g<sup>−1</sup>'' ∈ ''H'', then ''H'' is a normal subgroup of ''G'', (also expressed as "''H'' is invariant in ''G''"). That is, with5 KB (785 words) - 14:22, 30 July 2009
- In [[field theory]], a '''field automorphism''' is an [[automorphism]] of the [[algebraic structure]] of a [[field (mathematics)|field]], tha ...iven field ''K'' form a [[group (mathematics)|group]], the '''automorphism group''' <math>Aut(K)</math>.3 KB (418 words) - 17:18, 20 December 2008
- In mathematics, '''groups''' often arise as structures representing the set of possible symmetries o ...bined, and the full group of symmetries is called the 2-dimensional affine group. [[Felix Klein]] pioneered this approach to geometry, calling it the [[Erla15 KB (2,535 words) - 01:29, 15 February 2010
- ...' 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>\sigm Any characteristic subgroup of a group is [[normal subgroup|normal]], but the converse does not always hold.2 KB (358 words) - 07:37, 18 November 2008
- {{r|Normal subgroup}} {{r|Center (group theory)}}656 B (94 words) - 17:34, 8 November 2008
- ...bset of elements which [[commutativity|commute]] with every element of the group. ...[[group homomorphism|homomorphism]] to ''G'' to its [[inner automorphism]] group.785 B (114 words) - 16:29, 13 February 2009
- {{r|Field automorphism}} {{r|Group (mathematics)}}1 KB (146 words) - 21:32, 11 January 2010
- {{r|Automorphism}} {{r|Group theory}}2 KB (247 words) - 11:00, 7 November 2010
- ...mie française]] so that he could tell them how to define ''[[automorphic|automorphe]]'' in their dictionary. But there is a reason for special notation and t ...d but that they do not coincide. In practice, mathematicians are typically grouped with scientists at the gross level but separated at finer levels. This is30 KB (4,282 words) - 03:44, 11 June 2010