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algebraically compact group

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  • Algebraically compact group — In mathematics, in the realm of Abelian group theory, a group is said to be algebraically compact if it is a direct summand of every Abelian group containing it as a pure subgroup.Equivalent characterizations of algebraic compactness: * The group …   Wikipedia

  • Algebraically compact module — In mathematics, especially in the area of abstract algebra known as module theory, algebraically compact modules, also called pure injective modules, are modules that have a certain nice property which allows the solution of infinite systems of… …   Wikipedia

  • Group representation — In the mathematical field of representation theory, group representations describe abstract groups in terms of linear transformations of vector spaces; in particular, they can be used to represent group elements as matrices so that the group… …   Wikipedia

  • Compact operator on Hilbert space — In functional analysis, compact operators on Hilbert spaces are a direct extension of matrices: in the Hilbert spaces, they are precisely the closure of finite rank operators in the uniform operator topology. As such, results from matrix theory… …   Wikipedia

  • Cotorsion group — In mathematics, in the realm of abelian group theory, an abelian group is said to be cotorsion if every extension of it by a torsion free group splits. If the group is C, this is equivalent to asserting that Ext(G,C) = 0 for all torsion free… …   Wikipedia

  • Covering group — This article is about topological covering group. For algebraic covering group, see universal perfect central extension. In mathematics, a covering group of a topological group H is a covering space G of H such that G is a topological group and… …   Wikipedia

  • Abelian group — For other uses, see Abelian (disambiguation). Abelian group is also an archaic name for the symplectic group Concepts in group theory category of groups subgroups, normal subgroups group homomorphisms, kernel, image, quotient direct product,… …   Wikipedia

  • Paratopological group — In mathematics, a paratopological group is a topological semigroup G which is algebraically a group. [Artur Hideyuki Tomita. [http://tatra.mat.savba.sk/Full/14/10tomita.ps On sequentially compact both sides cancellative semigroups with… …   Wikipedia

  • Lie group — Lie groups …   Wikipedia

  • Compactly generated group — In mathematics, a compactly generated (topological) group is a topological group G which is algebraically generated by one of its compact subsets. Explicitly, this means that there exists a compact subset K of G such that So if K is symmetric,… …   Wikipedia

  • Special unitary group — In mathematics, the special unitary group of degree n , denoted SU( n ), is the group of n times; n unitary matrices with determinant 1. The group operation is that of matrix multiplication. The special unitary group is a subgroup of the unitary… …   Wikipedia

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