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...-theorem''' is a result in [[Group theory#Finite group theory|finite group theory]] formerly known as the '''B-conjecture'''. ...|centralizer]] of an [[involution (mathematics)|involution]] of a [[finite group]], then every component of <math>C/O(C)</math> is the image of a component ...

...entary for some [[prime number]] ''p''. An elementary group is [[nilpotent group|nilpotent]]. ...auer's theorem on induced characters]] states that a character on a finite group is a linear combination with integer coefficients of characters [[induced c ...

...main theorems in [[local class field theory]] states that the norm groups in <math>K^\times</math> are precisely the open subgroups of <math>K^\times</m *J.S. Milne, ''Class field theory.'' Version 4.01. ...

....}}</ref> The theorems are among the most important results of [[invariant theory]]. ...bitrary characteristic.<ref>{{harvnb|Procesi|2007|loc=Ch. 13 develops this theory.}}</ref> ...

{{short description|Asymptotic estimate in group theory}} In [[finite group|finite group theory]], the '''Higman–Sims asymptotic formula''' gives an asymptotic estimate on ...

In mathematical finite group theory, the '''L-balance theorem''' was proved by {{harvtxt|Gorenstein|Walter|1975 The letter ''L'' stands for the [[layer (group theory)|layer]] of a group, and "balance" refers to the property discussed below. ...

{{short description|Conjecture in group theory}} ...the length of any [[orbit (group theory)|orbit]] of <math>G_\alpha</math> in the set <math>S \setminus \{\alpha\}</math>. ...

...extension theorem''' is a result from [[measure theory]] and [[probability theory]] on extensions of [[probability measure]]s. The theorem makes a statement .../ref> The general case was shown by [[Albert Ascherl]] and [[Jürgen Lehn]] in 1977.<ref name="al">{{cite journal |first1=Albert |last1=Ascherl |first2=Jü ...

...ath> are denoted <math>\text{Aut}(\mathfrak{g})</math>, the [[automorphism group]] of <math>\mathfrak{g}</math>. ...atorname{Aut}^0(\mathfrak{g})</math> is known as the '''outer automorphism group'''.<ref>{{harvnb|Humphreys|1972}}</ref> ...

{{Short description|Criterion for vector stability in algebraic geometry}} ...vector is stable if and only if the norm attains a minimum value on the [[Group action (mathematics)|orbit]] of the vector. ...

...)|link]]s. The conditions are stated in terms of the [[group (mathematics)|group]] structures on braids. ...ates that every [[knot (mathematics)|knot]] or [[link (knot theory)|link]] in three-dimensional Euclidean space is the closure of a [[braid (mathematics) ...

...bout it (reproduced in {{harv|Dedekind|1968}}, with an English translation in {{harv|Curtis|2003|loc=p.&nbsp;51}}). If one takes the multiplication table of a finite [[Group (mathematics)|group]] ''G'' and replaces each entry ''g'' with the variable ''x''<sub>''g''</su ...

{{short description|Result in algebraic K-theory relating Chow groups to cohomology}} ...ield]] is isomorphic to the cohomology of ''X'' with coefficients in the K-theory of the structure sheaf <math>\mathcal{O}_X</math>; that is, ...

...Serre]] to give a description of the structure of the corresponding matrix group over the [[coordinate ring]] of a [[projective curve]]. ...'R'', and let ''R''^* denote the [[Group of units#Group of units|group of units]] of ''R'', and let ...

...me ''X'' with [[linear algebraic group action|action of a linear algebraic group]] ''G'', via Quillen's [[Q-construction]]; thus, by definition, ...2–1995)].</ref> Specifically, he proved equivariant analogs of fundamental theorems such as the localization theorem. ...

...is realised in a certain space, of [[square-integrable function]]s, given in a concrete way. ...n]] of a [[Group (mathematics)|group]] ''G'' to a [[subgroup]]&nbsp;''H''. In that context, the pair (''G'',&nbsp;''H'') is called a strong [[Gelfand pai ...

...ization]] in the full quantum theory. Renormalization theorems are common in theories with a sufficient amount of [[supersymmetry]], usually at least 4 ...ntroduced by [[Marcus T. Grisaru]], [[Martin Rocek]] and [[Warren Siegel]] in their 1979 paper [http://www.slac.stanford.edu/spires/find/hep/www?j=NUPHA, ...

{{short description|On the connectivity of a group of diffeomorphisms of a manifold}} ...m''' is a theorem of [[Jean Cerf]]'s which refers to the connectivity of a group of [[Diffeomorphism|diffeomorphisms]] of a manifold. ...

{{DISPLAYTITLE:Fundamental theorem of algebraic ''K''-theory}} ...ebra]], the '''fundamental theorem of [[algebraic K-theory|algebraic ''K''-theory]]''' describes the effects of [[change of rings|changing the ring]] of ''K' ...

...is a [[special function|special]] spherical function on a [[semisimple Lie group]], studied by {{harvs|txt|last=Harish-Chandra|authorlink=Harish-Chandra|yea *''K'' is a maximal compact subgroup of a semisimple Lie group with [[Iwasawa decomposition]] ''G''=''NAK'' ...