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...s]], the '''B-theorem''' is a result in [[Group theory#Finite group theory|finite group theory]] formerly known as the '''B-conjecture'''. ...k|last1=Gorenstein|first1=Daniel|title=The Classification of finite simple groups|date=1983|publisher=Plenum Press|location=New York|isbn=978-0-306-41305-6|p ...

...theory)|order]] relatively prime to ''p'' and a [[p-group|''p''-group]]. A finite group is an elementary group if it is ''p''-elementary for some [[prime num [[Brauer's theorem on induced characters]] states that a character on a finite group is a linear combination with integer coefficients of characters [[ind ...

In mathematical finite group theory, the '''L-balance theorem''' was proved by {{harvtxt|Gorenstei The L-balance theorem of Gorenstein and Walter states that if ''X'' is a finite group and ''T'' a 2-subgroup of ''X'' then ...

...igman–Sims asymptotic formula''' gives an asymptotic estimate on number of groups of prime power order. ...mber]]. Define <math>f(n,p)</math> as the number of isomorphism classes of groups of order <math>p^n</math>. Then: ...

...\times</math> are precisely the open subgroups of <math>K^\times</math> of finite index. ...

...ecture]]d that if <math>G</math> is a [[primitive permutation group]] on a finite set <math>S</math> and <math>G_\alpha</math> denotes the [[stabilizer (grou ...Jan Saxl]], and [[Gary Seitz]] using the [[classification of finite simple groups]], in particular the fact that only finitely many [[isomorphism]] types of ...

...nd the relations).<ref>{{harvnb|Procesi|2007|loc=Ch. 9, § 1.4.}}</ref> The theorems are among the most important results of [[invariant theory]]. ...haracteristic (algebra)|characteristic]]-free invariant theory extends the theorems to a [[field (mathematics)|field]] of arbitrary characteristic.<ref>{{harvn ...

...tion that is either degenerate or is representable as the convolution of a finite or countable set of indecomposable distributions. The factorization is not ...onvolution semi-group of distributions on the line, in which factorization theorems analogous to Khinchin's theorem are valid. ...

...khin A. L.|date=1970|title=Certain statistical and probability problems on groups|journal=Trudy Mat. Inst. Steklov|volume=111|pages=52–109}}</ref><ref>{{Cite == An extension to locally compact Abelian groups == ...

{{short description|On the effects of changing the ring of ''K''-groups}} ...an Bass]] for <math>K_0, K_1</math> and was later extended to higher ''K''-groups by [[Daniel Quillen]]. ...

{{short description|Lifts an action of a finite-dimensional Lie algebra on a manifold to a Lie group action}} ...th>M</math> can be integrated to a [[Lie group action|smooth action]] of a finite-dimensional [[Lie group]] <math>G</math>, i.e. there is a smooth action <ma ...

| title=Rings of invariants of reductive groups acting on regular rings are Cohen-Macaulay ...ials <math>f_1, \cdots, f_d</math> such that <math>k[V]^G</math> is a free finite [[graded module]] over <math>k[f_1, \cdots, f_d]</math>. ...

...''i''&nbsp;≥&nbsp;3. Therefore, the Euler characteristic only involves the groups with ''i''&nbsp;=&nbsp;0,&nbsp;1,&nbsp;2. ===Case of finite modules=== ...

...c structure of [[subgroup]]s of [[free product]]s of [[group (mathematics)|groups]]. The theorem was obtained by [[Aleksandr Gennadievich Kurosh|Alexander Ku ...raham Karrass and Donald Solitar, ''The subgroups of a free product of two groups with an amalgamated subgroup.'' ...

...996|loc=Theorem 7.2.6.}}</ref><ref name="9.4 and 9.5">{{harvnb|Hall|2015}} Theorems 9.4 and 9.5</ref> There is a closely related theorem classifying the [[Comp ...Lie Group Theory, Andrew Baker; Lie Groups: An Introduction through Linear Groups, Wulf Rossmann|journal=The American Mathematical Monthly|year=2003|volume=1 ...

...ory)|order]] of the [[centralizer and normalizer|normalizer]] of a [[Sylow theorems|Sylow <math>p</math>-subgroup]]. ...general conjecture for any prime value of <math>p</math> and more general groups. ...

...theorem''', which describes the classification of certain infinite abelian groups in terms of their '''Ulm factors''' or '''Ulm invariants'''. ...factor ''U''_''σ''(''A'') the ''p''-heights of its elements are finite and they are unbounded for every Ulm factor except possibly the last one, n ...

...several related theorems regarding the sizes of certain sumsets in abelian groups}} ...ombinatorics]], '''Kneser's theorem''' can refer to one of several related theorems regarding the sizes of certain [[sumset]]s in [[abelian group]]s. These are ...

...orem is a key tool in one of the quickest proofs of amenability of abelian groups. ...sets <math>K^T</math> as <math>T</math> ranges over the subset. From the [[finite intersection property|compactness]] of <math>K</math> it follows that the s ...

...ath> be functors on the category ''C'' of schemes separated and locally of finite type over the base field ''k'' with [[proper morphism]]s such that ...y situations to the Riemann–Roch theorem for [[quotient stack]]s by finite groups. ...