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...rd Brauer]] and [[Cecil J. Nesbitt]] in the [[representation theory]] of [[finite group]]s. ...is divisible by the highest power of a prime ''p'' dividing the order of a finite group remains irreducible when reduced mod ''p'' and vanishes on all elemen ...

Several theorems proved by the French [[mathematician]] [[Claude Chevalley]] bear his name. * [[Chevalley–Shephard–Todd theorem]] in [[invariant theory]] of [[finite group]]s. ...

{{short description|Quasisimple subnormal subgroup of a finite group}} ...], in the field of [[group theory]], a '''component''' of a [[finite group|finite]] [[group (mathematics)|group]] is a [[quasisimple group|quasisimple]] [[su ...

{{Short description|On the finite presentability of fundamental groups of 3-manifolds}} ...theorem about the [[Mapping class group of a surface#Finite presentability|finite presentability]] of [[fundamental group]]s of [[3-manifold]]s due to [[G. P ...

...roup]]s, [[Carter subgroup]]s, and [[abelian subgroup]]s of locally finite groups have been studied. The concept is credited to work in the 1930s by Russian ...nitely generated group|finitely generated]] [[subgroup]] is [[finite group|finite]]. ...

...|index]], so that the [[discrete space|discrete]] quotient group is always finite. ...be the [[inverse limit]] of an [[inverse system]] of discrete finite ''p''-groups. ...

...arify span|computable complete set of invariants|reason=Shouldn't this be "finite set of computable invariants"? Computability (whatever this is supposed to There exist many '''classification theorems''' in [[mathematics]], as described below. ...

...d Wright}}</ref> Some of these are [[Classification theorem|classification theorems]] of objects which are mainly dealt with in the field. For instance, the [[ ==Fundamental theorems of mathematical topics== ...

...=Solomon |title=A Brief History of the Classification of the Finite Simple Groups |journal=Bulletin of the American Mathematical Society |volume=38 |number=3 [[Category:Finite groups]] ...

...s]] ''g'' > 1. The simplest is that the [[automorphism]] group of ''X'' is finite (see though [[Hurwitz's automorphisms theorem]]). More generally, *the set of non-constant [[morphism]]s from ''X'' to ''Y'' is finite; ...

| title = The theory of nilpotent groups ...that the [[Fitting subgroup]] of certain types of groups (including all [[finite group]]s) is nilpotent. However, a subgroup generated by an ''infinite'' co ...

...te category ''J''). Dually, a category is '''finitely cocomplete''' if all finite colimits exist. ==Theorems== ...

...an]] from the 1960s.<ref> Graham Higman, ''Subgroups of finitely presented groups.'' Proceedings of the Royal Society. Series A. Mathematical and Physical S ...somorphism) exactly the finitely generated subgroups of finitely presented groups. ...

...is an important [[Lemma (mathematics)|lemma]] in the structure theory of [[finite group]]s. It is named after [[Giovanni Frattini]], who used it in a paper If <math>G</math> is a finite group with normal subgroup <math>H</math>, and if <math>P</math> is a [[Syl ...

{{Short description|Theorem that finite subgroups of mapping class groups can act on surfaces}} ...ear=1932|loc=pp. 147–148}} about whether finite subgroups of mapping class groups can act on surfaces, that was answered positively by {{harvs|txt|authorlin ...

{{short description|Mathematical group based upon a finite number of elements}} ...ber of structure-preserving transformations. Important examples of finite groups include [[cyclic group]]s and [[permutation group]]s. ...

...rrespondence between finite abelian extensions and generalized ideal class groups}} ...a fixed [[algebraic closure]] of ''K'') and the '''generalized ideal class groups''' defined via a '''modulus''' of ''K''. ...

...ch space|Banach spaces]], which resembles the [[Lebesgue measure]] used in finite-dimensional spaces. ...s like the [[Hilbert cube]], or scenarios where some typical properties of finite-dimensional Lebesgue measures are modified or omitted. ...

In [[abstract algebra]], '''Ado's theorem''' is a theorem characterizing finite-dimensional [[Lie algebra]]s. ...rem states that ''L'' has a [[linear representation]] ρ over ''K'', on a [[finite-dimensional vector space]] ''V'', that is a [[faithful representation]], ma ...

In algebraic group theory, '''approximation theorems''' are an extension of the [[Chinese remainder theorem]] to [[algebraic gro {{harvtxt|Eichler|1938}} proved strong approximation for some classical groups. ...