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nontrivial decomposition

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  • Modular decomposition — In graph theory, the modular decomposition is a decomposition of an undirected graph into subsets of vertices called modules. A module is a generalization of a connected component of a graph. Unlike connected components, however, one module can… …   Wikipedia

  • Stallings theorem about ends of groups — In the mathematical subject of group theory, the Stallings theorem about ends of groups states that a finitely generated group G has more than one end if and only if the group G admits a nontrivial decomposition as an amalgamated free product or… …   Wikipedia

  • Bass–Serre theory — is a part of the mathematical subject of group theory that deals with analyzing the algebraic structure of groups acting by automorphisms on simplicial trees. The theory relates group actions on trees with decomposing groups as iterated… …   Wikipedia

  • Grushko theorem — In the mathematical subject of group theory, the Grushko theorem or the Grushko Neumann theorem is a theorem stating that the rank (that is, the smallest cardinality of a generating set) of a free product of two groups is equal to the sum of the… …   Wikipedia

  • Satellite knot — In the mathematical theory of knots, a satellite knot is a knot which contains an incompressible, non boundary parallel torus in its complement [Colin Adams, The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots , (2001),… …   Wikipedia

  • Mayer–Vietoris sequence — In mathematics, particularly algebraic topology and homology theory, the Mayer–Vietoris sequence is an algebraic tool to help compute algebraic invariants of topological spaces, known as their homology and cohomology groups. The result is due to… …   Wikipedia

  • Dilworth's theorem — In mathematics, in the areas of order theory and combinatorics, Dilworth s theorem characterizes the width of any finite partially ordered set in terms of a partition of the order into a minimum number of chains. It is named for the mathematician …   Wikipedia

  • List of algebraic structures — In universal algebra, a branch of pure mathematics, an algebraic structure is a variety or quasivariety. Abstract algebra is primarily the study of algebraic structures and their properties. Some axiomatic formal systems that are neither… …   Wikipedia

  • Outline of algebraic structures — In universal algebra, a branch of pure mathematics, an algebraic structure is a variety or quasivariety. Abstract algebra is primarily the study of algebraic structures and their properties. Some axiomatic formal systems that are neither… …   Wikipedia

  • Representation theory — This article is about the theory of representations of algebraic structures by linear transformations and matrices. For the more general notion of representations throughout mathematics, see representation (mathematics). Representation theory is… …   Wikipedia

  • Krohn–Rhodes theory — In mathematics and computer science, Krohn Rhodes theory is an approach to the study of finite semigroups and automata that seeks to decompose them in terms of elementary components. These turn out to correspond to finite aperiodic semigroups and …   Wikipedia

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