In mathematics, a group is called boundedly generated if it can be expressed as a finite product of cyclic subgroups. The property of bounded generation is also closely related with the congruence subgroup problem (see Lubotzky & Segal 2003).
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are boundedlygenerated, then so is G itself. Any quotient group of a boundedlygeneratedgroup is also boundedlygenerated. A finitely generated torsion...
-Selmer groups of elliptic curves E / Q {\displaystyle E/\mathbb {Q} } respectively. Bhargava and Shankar's unconditional proof of the boundedness of the...
{\displaystyle i:X\to \mathbb {P} _{\mathbb {Z} }^{n}} gives the globally generated sheaf i ∗ O P Z n ( 1 ) {\displaystyle i^{*}{\mathcal {O}}_{\mathbf {P}...
strings, or whether one generates a subset of the strings generated by the other, or whether there is any string at all that both generate. The problem of determining...
generated by the (degree 2) Eisenstein series E4 and E6 and 3 more forms of weights 10, 12, and 35. The ideal of relations between them is generated by...
then the limit is also holomorphic. The uniform boundedness principle states that a pointwise bounded family of continuous linear operators between Banach...
(KPN, or process network) is a distributed model of computation in which a group of deterministic sequential processes communicate through unbounded first...
object in a preadditive category. The endomorphisms of a nonabelian groupgenerate an algebraic structure known as a near-ring. Every ring with one is...
{\displaystyle Cr_{2}(\mathbb {C} )} is generated by the "quadratic transformation" [x,y,z] ↦ [1/x, 1/y, 1/z] together with the group P G L ( 3 , C ) {\displaystyle...
(structurally) bounded if it is bounded for every possible initial marking. A Petri net is bounded if and only if its reachability graph is finite. Boundedness is...
spaces. They can be defined as topological vector spaces whose topology is generated by translations of balanced, absorbent, convex sets. Alternatively they...
key characteristics of a team include a shared goal, interdependence, boundedness, stability, the ability to manage their own work and internal process...
topology The topology of a space X is an Alexandrov topology (or is finitely generated) if arbitrary intersections of open sets in X are open, or equivalently...
sign. This means that although the local geometries of spacetime are generated by the theory of relativity based on spacetime intervals, we can approximate...
group is a certain group of unitary operators on the Hilbert space L2(R) of square integrable complex valued functions f on the real line, generated by...
only bounded operator on L2 with these properties. In fact there is a wider set of operators that commute with the Hilbert transform. The group SL ( 2...
{\displaystyle \Psi _{1}} norm is said to be "sub-exponential". Indeed, the boundedness of the Ψ p {\displaystyle \Psi _{p}} norm characterizes the limiting...
irrational in the remaining part of their actions. In another work, he states "boundedly rational agents experience limits in formulating and solving complex problems...
}\int _{\Omega }\left|f(x)-f_{k}(x)\right|^{p}\,{d\mu (x)}=0.} Imposing boundedness conditions not only on the function, but also on its derivatives leads...
unitary operators form a group under composition, which is the isometry group of H. An element of B(H) is compact if it sends bounded sets to relatively compact...
space looks the same at every point. All topological groups are homogeneous. Finitely generated or Alexandrov. A space X is Alexandrov if arbitrary intersections...
(1975) bargaining solutions emerge from the decentralized actions of boundedly rational agents without common knowledge. Whereas evolutionary game theory...
splittings of group homomorphisms from fundamental groups of complete smooth curves over finitely-generated fields k {\displaystyle k} to the Galois group of k...
a conventional probability distribution; and, conversely, satisfies boundedness properties unavailable to classical distributions. For instance, the...
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