lattice of subgroup
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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
Lattice — may refer to: In art and design: Latticework an ornamental criss crossed framework, an arrangement of crossing laths or other thin strips of material Lattice (pastry) In engineering: A lattice shape truss structure In mathematics: Lattice (order) … Wikipedia
Lattice (group) — A lattice in the Euclidean plane. In mathematics, especially in geometry and group theory, a lattice in Rn is a discrete subgroup of Rn which spans the real vector space Rn. Every lattice in Rn … Wikipedia
Lattice (mathematics) — In mathematics, the term lattice can mean:* A partially ordered set (poset) in which any two elements have a supremum and an infimum mdash;see lattice (order). The Hasse diagrams of these posets look (in some simple cases) like the lattices of… … Wikipedia
Lattice of subgroups — In mathematics, the lattice of subgroups of a group G is the lattice whose elements are the subgroups of G, with the partial order relation being set inclusion.In this lattice, the join of two subgroups is the subgroup generated by their union,… … Wikipedia
Subgroup — This article is about the mathematical concept For the galaxy related concept, see Galaxy subgroup. Concepts in group theory category of groups subgroups, normal subgroups group homomorphisms, kernel, image, quotient direct product, direct sum … Wikipedia
Lattice theorem — In mathematics, the lattice theorem, sometimes referred to as the fourth isomorphism theorem or the correspondence theorem, states that if N is a normal subgroup of a group G, then there exists a bijection from the set of all subgroups A of G… … Wikipedia
Subgroup series — In mathematics, a subgroup series is a chain of subgroups: Subgroup series can simplify the study of a group to the study of simpler subgroups and their relations, and several subgroup series can be invariantly defined and are important… … Wikipedia
Lattice group — In mathematics, the term lattice group is used for two distinct notions:* a lattice, a discrete subgroup of R n and its generalizations.* a lattice ordered group, a group that with a partial ordering that is a lattice order … Wikipedia
Maximal subgroup — Lattice of subgroups of the symmetric group S4 M. s. are A4, three Dih4 and four S3 (Compare: Subgroups of S … Wikipedia
E₈ lattice — In mathematics, the E8 lattice is a special lattice in R8. It can be characterized as the unique positive definite, even, unimodular lattice of rank 8. The name derives from the fact that it is the root lattice of the E8 root system. The normIn… … Wikipedia
