Discrete group
Discrete group In mathematics, a discrete group is a group G equipped with the discrete topology. With this topology G becomes a topological group. A discrete subgroup of a topological group G is ...
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Subgroup growth
Subgroup growth Im mathematics, subgroup growth is a branch of group theory ... and normal subgroups of index n, respectively. Subgroup growth studies these functions, their interplay, and ... As an example, let G be the discrete Heisenberg group. This group has a presentation ... a'b). To each finite index subgroup U of G, associate the set ...
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Small subgroup confinement attack
Small subgroup confinement attack In cryptography, a subgroup confinement attack (or small subgroup confinement attack) on a cryptographic method that ... to be confined to an unexpectedly small subgroup of the desired group. Several methods have been found to be vulnerable to subgroup confinement attack, including some forms or ...
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Dihedral group
... form one of the two series of discrete point groups in two dimensions. D n ... have considered D n to be a subgroup of O(2), i.e. the group ... D n is also used for a subgroup of SO(3) which is also of ... thus, Dih n always has a normal subgroup isomorphic to Z n ): Z n φ ... we see that Dih n is a subgroup of the symmetric group S n . ...
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Point groups in three dimensions
... group of a sphere. It is a subgroup of the orthogonal group O(3), the ... orthogonal matrices. O(3) itself is a subgroup of the Euclidean group E(3) of ... chiral. Group structure SO(3) is a subgroup of E + (3), which consists of direct ... group of direct isometries H has a subgroup L of index 2, then, apart from ... for every positive integer k a normal subgroup of O(2,R) and SO( ...
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List of mathematics articles (D-F)
... Diagonal intersection -- Diagonal lemma -- Diagonal matrix -- Diagonal subgroup -- Diagonalizable matrix -- Diagonalization -- Diagonalization lemma -- Diagram chasing ... linear map -- Discourse on Method -- Discrepancy function -- Discrete category -- Discrete cosine transform -- Discrete element method -- Discrete Fourier transform -- Discrete geometry -- Discrete group -- ...
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Euclidean plane isometry
... to rigid motions, and form a normal subgroup of the full Euclidean group of isometries ... Neither the full group nor the even subgroup are abelian; for example, reversing the order ... form a group, and even isometries a subgroup. (Odd isometries do not include the identity, so are not a subgroup.) This subgroup is a normal subgroup, because sandwiching ...
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Talk:Fuchsian group
... a Fuchsian group is a torsion-free discrete subgroup of PSL(2,R). It would be ... says a Fuchsian group is a discontinuous subgroup of PSL(2,R), then goes on ... another clause in the definition of "Fuchsian subgroup". Since I know a bunch of discontinuous ... torsion-free belongs in the definition. Yes, discrete subgroup in precisely what Lie group ...
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User:Mathbot/Changes mathlist
... form (statistics) Added Triple spiral Added Uniformly discrete set Added Vertical (angles) Feb 22 Removed ... Colloquium (College of Engineering, Guindy) Added Commutator subgroup Added Fitting's theorem Added Gentzen's ... Rotation number Added Schreier vector Added Small subgroup confinement attack Added Special right triangles Added ... Connector Added Generalised logistic curve Added Hidden subgroup problem Added Jackson's theorem Added MEF ... Added UV fixed point Jan 27 Removed Discrete Hankel transform/Temp Removed Peter B. ...
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Fuchsian group
... plane. A Fuchsian group is always a discrete group, and thus is a lattice in ... be made, defining it to be a discrete group or as group that acts properly ... group can be defined to be a subgroup of either PSL(2,R) or PSL ... open unit disk. In either case, a subgroup that is conjugate (in PSL(2,C ... following three properties hold: Γ is a discrete group (with respect to the standard ...
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