In mathematics, the finite lattice representation problem, or finite congruence lattice problem, asks whether every finite lattice is isomorphic to the congruence lattice of some finite algebra.
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Farrell–Jones conjecture Finitelatticerepresentationproblem: is every finitelattice isomorphic to the congruence lattice of some finite algebra? Goncharov...
as an intersection of a finite number of half-spaces. Such definition is called a half-space representation (H-representation or H-description). There...
complete lattice. For comparison, in a general lattice, only pairs of elements need to have a supremum and an infimum. Every non-empty finitelattice is complete...
for the solution, which has a finite number of points. The finite element method formulation of a boundary value problem finally results in a system of...
becomes finite-dimensional, and can be evaluated by stochastic simulation techniques such as the Monte Carlo method. When the size of the lattice is taken...
The Burnside problem asks whether a finitely generated group in which every element has finite order must necessarily be a finite group. It was posed by...
an instance of the hidden subgroup problem for finite abelian groups, while the other problems correspond to finite groups that are not abelian. Given...
the lattice of stable matchings is a distributive lattice whose elements are stable matchings. For a given instance of the stable matching problem, this...
structure of a finite simple group. Another suggestion for simplifying the proof is to make greater use of representation theory. The problem here is that...
congruence latticeproblem asks whether every algebraic distributive lattice is isomorphic to the congruence lattice of some other lattice. The problem was posed...
apparent already on a relatively small lattice, even though the singularities are smoothed out by the system's finite size. This was first established by...
invariant under T is ostensibly a problem of geometric nature. Matrix representation allows one to phrase this problem algebraically. Write V as the direct...
finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any field, a finite...
the fundamental theorem of finitely generated abelian groups it is therefore a finite direct sum of copies of Z and finite cyclic groups. The proof of...
forms a representation of a subgroup using a known representation of the whole group. Restriction is a fundamental construction in representation theory...
abelian groups of finite rank, only the finitely generated case and the rank 1 case are well understood; There are many unsolved problems in the theory of...
phonology (e.g. optimality theory, which uses lattice graphs) and morphology (e.g. finite-state morphology, using finite-state transducers) are common in the analysis...
group Dicyclic group Dihedral group Divisible group Finitely generated abelian group Group representation Klein four-group List of small groups Locally cyclic...
related finite group Co0 introduced by (Conway 1968, 1969). The largest of the Conway groups, Co0, is the group of automorphisms of the Leech lattice Λ with...
be a finite-dimensional K-algebra. An order in AK is an R-subalgebra that is a lattice. In general, there are a lot fewer orders than lattices; e.g....
is residually finite. An important question regarding the algebraic structure of arithmetic groups is the congruence subgroup problem, which asks whether...
algebraic group G over a perfect field is reductive if it has a representation that has a finite kernel and is a direct sum of irreducible representations....
in the early 20th century, representation theory, and many more influential spin-off domains. The classification of finite simple groups is a vast body...
the set of all structurally complete finite automata generating a given input set of example strings forms a lattice, with the trivial undergeneralized...
effort, the classification of finite simple groups was declared accomplished in 1983 by Daniel Gorenstein, though some problems surfaced (specifically in...
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