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searching for Semidirect product 25 found (155 total)

Markov kernel (2,052 words) [view diff] no match in snippet view article find links to article

In probability theory, a Markov kernel (also known as a stochastic kernel or probability kernel) is a map that in the general theory of Markov processes

Class automorphism (259 words) [view diff] exact match in snippet view article find links to article

groups, the classical example is a group of order 32 obtained as the semidirect product of the cyclic ring on 8 elements, by its group of units acting via

Free-by-cyclic group (833 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \varphi } is an automorphism of F {\displaystyle F} , the semidirect product F ⋊ φ Z {\displaystyle F\rtimes _{\varphi }\mathbb {Z} } is a free-by-cyclic

Langlands dual group (936 words) [view diff] exact match in snippet view article find links to article

induced action of the Galois group Gal(K/k). The full L-group LG is the semidirect product LG = LGo×Gal(K/k) of the connected component with the Galois group

Frobenioid (417 words) [view diff] exact match in snippet view article find links to article

of N multiplying an element of M by n. The Frobenioid of M is the semidirect product of M and N. The underlying category of this Frobenioid is category

Snake lemma (1,524 words) [view diff] exact match in snippet view article find links to article

group S 3 {\displaystyle S_{3}} , which in turn can be written as a semidirect product of cyclic groups: S 3 ≃ C 3 ⋊ C 2 {\displaystyle S_{3}\simeq C_{3}\rtimes

Aschbacher block (270 words) [view diff] exact match in snippet view article find links to article

L acts irreducibly on U/CU(L) An example of a short group is the semidirect product of a quasisimple group with an irreducible module over the 2-element

Dade isometry (417 words) [view diff] exact match in snippet view article find links to article

lifting is an isometry if for each k ∈ K, the centralizer CG(k) is the semidirect product of a normal Hall π' subgroup I(K) with CH(k). The Feit–Thompson proof

Geometrization conjecture (4,050 words) [view diff] exact match in snippet view article find links to article

point stabilizer is O(2, R). The group G has 2 components, and is a semidirect product of the 3-dimensional Heisenberg group by the group O(2, R) of isometries

Complex Lie algebra (830 words) [view diff] exact match in snippet view article find links to article

{b}}={\mathfrak {h}}\oplus {\mathfrak {n}}^{+}} is closed and is the semidirect product of H {\displaystyle H} and U {\displaystyle U} ; the conjugates of

Klein bottle (2,908 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \mathbb {Z} \rtimes \mathbb {Z} } , the only nontrivial semidirect product of the additive group of integers Z {\displaystyle \mathbb {Z} } with

Cremona group (1,122 words) [view diff] exact match in snippet view article find links to article

transformations fixing a pencil of lines through a given point, and is the semidirect product of P G L 2 ( k ) {\displaystyle \mathrm {PGL} _{2}(k)} and P G L 2

Representation theory of finite groups (21,307 words) [view diff] exact match in snippet view article find links to article

presented theory to normal subgroups and to a special group, the semidirect product of a subgroup with an abelian normal subgroup. Proposition. Let A

Delaram Kahrobaei (1,407 words) [view diff] exact match in snippet view article find links to article

1515/gcc-2018-0006. Kahrobaei, D.; Shpilrain, V. (2016). "Invited Paper: Using semidirect product of (semi)groups in public key cryptography". Computability in Europe

Universal embedding theorem (953 words) [view diff] exact match in snippet view article find links to article

are both in H. This is an automorphism of K, so we can define the semidirect product K ⋊ H called the regular wreath product, and denoted A Wr H or A ≀

Brauer's k(B) conjecture (433 words) [view diff] exact match in snippet view article

group automorphisms. Let G V {\displaystyle GV} denote the associated semidirect product and let k ( G V ) {\displaystyle k(GV)} be its number of conjugacy

List of XML and HTML character entity references (3,509 words) [view diff] exact match in snippet view article find links to article

ISOamsb left normal factor semidirect product (left times) &rtimes; ⋊ U+22CA HTML 5.0 ISOamsb right normal factor semidirect product (right times) &lthree;

Feit–Thompson theorem (2,854 words) [view diff] exact match in snippet view article find links to article

(pq–1)/(p–1) is coprime to p–1 and G has a subgroup given by the semidirect product PU where P is the additive group of a finite field of order pq and

Affine gauge theory (1,940 words) [view diff] exact match in snippet view article find links to article

, R ) {\displaystyle GA(n,\mathbb {R} )} so that the latter is a semidirect product of G L ( n , R ) {\displaystyle GL(n,\mathbb {R} )} and a group T

Lie's theorem (2,644 words) [view diff] exact match in snippet view article find links to article

p-dimensional vector space k[x]/(xp), which has no eigenvectors. Taking the semidirect product of this 3-dimensional Lie algebra by the p-dimensional representation

Hermitian symmetric space (7,418 words) [view diff] exact match in snippet view article find links to article

{l}}={\mathfrak {k}}\otimes \mathbb {C} } . The Lie algebra of P is the semidirect product m + ⊕ l {\displaystyle {\mathfrak {m}}^{+}\oplus {\mathfrak {l}}}

Semisimple Lie algebra (5,731 words) [view diff] exact match in snippet view article find links to article

decomposition, which states that every finite dimensional Lie algebra is the semidirect product of a solvable ideal (its radical) and a semisimple algebra. In particular

List of finite simple groups (1,789 words) [view diff] exact match in snippet view article find links to article

outer automorphism group is often, but not always, isomorphic to the semidirect product D ⋊ ( F × G ) {\displaystyle D\rtimes (F\times G)} where all these

Complex affine space (2,538 words) [view diff] exact match in snippet view article find links to article

group of A. It is isomorphic (but not naturally isomorphic) to a semidirect product of the group GL(V) and V. The subgroup GL(V) is the stabilizer of

Schwarzian derivative (6,967 words) [view diff] exact match in snippet view article find links to article

homomorphisms of groups: it is encoded in a homomorphism 𝜙 of G into the semidirect product M ⋊ G {\displaystyle M\rtimes G} such that the composition of 𝜙 with