Noetherian group

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• Noetherian — In mathematics, the adjective Noetherian is used to describe objects that satisfy an ascending or descending chain condition on certain kinds of subobjects; in particular, Noetherian group, a group that satisfies the ascending chain condition on… …   Wikipedia

• Polycyclic group — In mathematics, especially in the area of abstract algebra known as group theory, a polycyclic group is a solvable group that satisfies the maximal condition on subgroups (that is, every subgroup is finitely generated).Equivalently, a group G is… …   Wikipedia

• Prüfer group — In mathematics, specifically group theory, the Prüfer p group or the p quasicyclic group or p infin; group, Z( p infin;), for a prime number p is the unique torsion group in which every element has p p th roots.*The Prüfer p group may be… …   Wikipedia

• Divisible group — In mathematics, especially in the field of group theory, a divisible group is an abelian group in which every element can, in some sense, be divided by positive integers, or more accurately, every element is an nth multiple for each positive… …   Wikipedia

• Glossary of group theory — A group ( G , •) is a set G closed under a binary operation • satisfying the following 3 axioms:* Associativity : For all a , b and c in G , ( a • b ) • c = a • ( b • c ). * Identity element : There exists an e ∈ G such that for all a in G , e •… …   Wikipedia

• Emmy Noether — Amalie Emmy Noether Born 23 March 1882(1882 03 23) …   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

• Small cancellation theory — In the mathematical subject of group theory, small cancellation theory studies groups given by group presentations satisfying small cancellation conditions, that is where defining relations have small overlaps with each other. It turns out that… …   Wikipedia

• Ring (mathematics) — This article is about algebraic structures. For geometric rings, see Annulus (mathematics). For the set theory concept, see Ring of sets. Polynomials, represented here by curves, form a ring under addition and multiplication. In mathematics, a… …   Wikipedia

• Dedekind domain — In abstract algebra, a Dedekind domain or Dedekind ring, named after Richard Dedekind, is an integral domain in which every nonzero proper ideal factors into a product of prime ideals. It can be shown that such a factorization is then necessarily …   Wikipedia

• Injective module — In mathematics, especially in the area of abstract algebra known as module theory, an injective module is a module Q that shares certain desirable properties with the Z module Q of all rational numbers. Specifically, if Q is a submodule of some… …   Wikipedia