open subgroup
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Subgroup growth — Im mathematics, subgroup growth is a branch of group theory, dealing with quantitative questions about subgroups of a given group. [citebook|title=Subgroup Growth|author=Alexander Lubotzky, Dan Segal|year=2003|publisher=Birkhäuser|id=ISBN… … Wikipedia
Hidden subgroup problem — The hidden subgroup problem (HSP) is a topic of research in mathematics and theoretical computer science. Problem statementGiven a group G , a subgroup H ≤ G , and a set X , we say a function f : G → X separates cosets of H if for all g 1, g 2 ∈… … Wikipedia
Kurosh subgroup theorem — In the mathematical field of group theory, the Kurosh subgroup theorem descibes the algebraic structure of subgroups of free products of groups. The theorem was obtained by a Russian mathematician Alexander Kurosh in 1934. [A. G. Kurosh, Die… … Wikipedia
Lattice (discrete subgroup) — In Lie theory and related areas of mathematics, a lattice in a locally compact topological group is a discrete subgroup with the property that the quotient space has finite invariant measure. In the special case of subgroups of R n , this amounts … Wikipedia
Surface subgroup conjecture — In mathematics, the surface subgroup conjecture of Friedhelm Waldhausen states that the fundamental group of every closed, irreducible 3 manifold with infinite fundamental group has a surface subgroup. By surface subgroup we mean the fundamental… … Wikipedia
Symmetric space — In differential geometry, representation theory and harmonic analysis, a symmetric space is a smooth manifold whose group of symmetries contains an inversion symmetry about every point. There are two ways to make this precise. In Riemannian… … Wikipedia
Topological group — Concepts in group theory category of groups subgroups, normal subgroups group homomorphisms, kernel, image, quotient direct product, direct sum semidirect product, wreath product … Wikipedia
Class formation — In mathematics, a class formation is a structure used to organize the various Galois groups and modules that appear in class field theory. They were invented by Emil Artin and John Tate. Contents 1 Definitions 2 Examples of class formations 3 The … Wikipedia
Pro-p group — In mathematics, a pro p group (for some prime number p) is a profinite group G such that for any open normal subgroup the quotient group G / N is a p group. Note that, as profinite groups are compact, the open subgroup must be of finite index, so … Wikipedia
Admissible representation — In mathematics, admissible representations are a well behaved class of representations used in the representation theory of reductive Lie groups over real or p adic fields. They were introduced by Harish Chandra.Real reductive groupsFor real… … Wikipedia
Totally disconnected group — In mathematics, a totally disconnected group is a topological group that is totally disconnected. Such topological groups are necessarily Hausdorff.Interest centres on locally compact totally disconnected groups. The compact case has been heavily … Wikipedia
