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...ath> are denoted <math>\text{Aut}(\mathfrak{g})</math>, the [[automorphism group]] of <math>\mathfrak{g}</math>. == Inner and outer automorphisms == ...

...m |first4=Katherine |date=2010 |title=On the Fixed Points of Abelian Group Automorphisms |url=https://scholar.rose-hulman.edu/cgi/viewcontent.cgi?article=1126&conte ...ics)|set]] of automorphisms of ''G'' (i.e., a subset of the [[automorphism group]] of ''G''), then the set of the elements of ''G'' that are left fixed by e ...

{{Short description|Group of gauge symmetries in Yang–Mills theory}} ...ated group bundle <math> \widetilde P\to X</math> whose typical fiber is a group <math>G</math> which acts on itself by the [[adjoint representation]]. The ...

...[[Faithful action|faithful]] since <math>S</math> has a trivial [[Center (group theory)|center]].<ref>{{Cite journal |last1=Dallavolta |first1=F. |last2=Lu ...>\mathrm{S}_n</math> is the automorphism group of the simple [[alternating group]] <math>\mathrm{A}_n,</math> so <math>\mathrm{S}_n</math> is almost simple ...

| automorphisms = 896,690,995,200 ...r 896690995200 and contains as a subgroup of order 2 the [[Suzuki sporadic group]]. It is named for [[Michio Suzuki (mathematician)|Michio Suzuki]]. ...

{{Short description|Group representation via algebra automorphisms}} In mathematics, an '''algebraic representation''' of a [[group (mathematics)|group]] ''G'' on a [[algebra over a field|''k''-algebra]] ''A'' is a [[linear rep ...

...thematics]], general covariant transformations are defined as particular [[automorphisms]] of so-called natural [[fiber bundle]]s. ...[[Lie group|infinitesimal generator]] of a one-parameter [[Lie group]] of automorphisms of <math>Y</math> is a projectable [[vector field]] ...

...to define the [[Kirillov model]] of a representation of the general linear group. ...of {{mvar|k}} is a mirabolic subgroup of the 2-dimensional general linear group. ...

...k</math> is the field of complex numbers and <math>n</math>=2, the Cremona group contains an infinite non-countable family of different [[normal subgroup]]s * with [[Igor Dolgachev]]: Rational Surfaces with a Large Group of Automorphisms, J. Amer. Math. Soc., Vol. 25, 2012, pp.&nbsp;863–905. [https://arxiv.org/a ...

...]] and [[Petrie dual]]ity, and have the group structure of the [[symmetric group]] on three elements. They are named for Stephen E. Wilson, who published th ...ual. Together they constitute the [[Group (mathematics)|group]] [[Dihedral group of order 6|S3]]. ...

More generally, if ''G'' is a [[group (mathematics)|group]] [[group action|acting]] on ''R'', then the subring of ''R'' ...subring of an automorphism ''f'' is the ring of invariants of the [[cyclic group]] generated by ''f''. ...

| automorphisms= 2448 ([[projective special linear group|PSL]](2,17)) ...h. Therefore, the Biggs&ndash;Smith graph is a [[symmetric graph]]. It has automorphisms that take any vertex to any other vertex and any edge to any other edge. Ac ...

...Ualbai U. | last2=Shestakov | first2=Ivan P. | title=The tame and the wild automorphisms of polynomial rings in three variables | url=https://dx.doi.org/10.1090/S08 ...=Masayoshi | author1-link=Masayoshi Nagata | title=<nowiki>On automorphism group of k[x,y]</nowiki> | url=https://books.google.com/books?id=qvruAAAAMAAJ | p ...

{{short description|Mathematical group formed from the automorphisms of an object}} ...group <math>\operatorname{Aut}(X)</math> is the group consisting of all [[group automorphism]]s of ''X''. ...

| automorphisms= 78 &nbsp; (C13⋊C6) ...rtices.<ref name="COND"/> It is also a [[Cayley graph]] for the [[dihedral group]] ''D''₂₆, generated by ''a'', ''ab'', and ''ab''⁴, ...

..., it acts on the set <math>\pi^{-1}(x) \subset Y</math>. In fact, the only automorphisms of <math>\text{Fib}_x</math> come from <math>\pi_1(X,x)</math>. ...oup]], denoted <math>\pi_1(S,\overline{s})</math>, and induce a continuous group action on these finite fiber sets, giving an equivalence between covers and ...

...ic group]] <math>G</math> over a field <math>K</math> is another algebraic group <math>H</math> such that there exists an isomorphism <math>\phi</math> betw ...nn}(G))</math> where <math>\mathrm{Inn}(G)</math> is the subgroup of inner automorphisms of <math>G</math>. ...

...c number field]]s can be reduced to problems about their [[absolute Galois group]]s. ...number field correspond to [[outer automorphism]]s of its absolute Galois group. {{harvs|txt|last=Pop|first=Florian|authorlink=Florian Pop|year1=1990|year2 ...

...on of a [[pseudo-Anosov map|pseudo-Anosov element]] of the [[mapping class group]] of a finite type surface. Fully irreducibles play an important role in th ...educible''<ref>Thierry Coulbois and Arnaud Hilion, ''Botany of irreducible automorphisms of free groups'', [[Pacific Journal of Mathematics]] '''256''' (2012), 291– ...

...al]] field of infinite [[group theory]], the '''Nottingham group''' is the group ''J''('''F'''_''p'') or ''N''('''F'''_''p'') consistin with coefficients in '''F'''_''p''. The group multiplication is given by formal composition also called substitution. Tha ...