quasicyclic group

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• Abelian root group — If G is an abelian group and P is a set of primes then G is an abelian P root group if every element in G has a p th root for every prime p in P ::gin G,pin P Rightarrow exists hin G, h^p=g;(with the product written multiplicatively)If the set of …   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

• 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

• Hopfian group — In mathematics, a Hopfian group is a group G for which every epimorphism: G rarr; G is an isomorphism. Equivalently, a group is Hopfian if and only if it is not isomorphic to any of its proper quotients.Example of Hopfian groups* Every finite… …   Wikipedia

• Primary cyclic group — A primary cyclic group is a cyclic group of prime power order:C {p^m};(for any prime p , and natural number m ).Every finite abelian group G may be written as a finite direct sum of primary cyclic groups::G=igoplus {1leq i leq n}C p i}^{m i;This …   Wikipedia

• Artinian module — In abstract algebra, an Artinian module is a module that satisfies the descending chain condition on its submodules. They are for modules what Artinian rings are for rings, and a ring is Artinian if and only if it is an Artinian module over… …   Wikipedia

• Grupo de Prüfer — El 2 grupo de Prüfer. <gn: gn+12 = gn, g12 = e> En matemáticas, y en especial en teoría de grupos, el p grupo de Prüfer, grupo p cuasicíclico o el p∞ grupo, Z(p∞), para un número primo p es el único …   Wikipedia Español

• Krull-Schmidt theorem — In mathematics, the Krull Schmidt theorem states that a group G, subjected to certain finiteness conditions of chains of subgroups, can be uniquely written as a finite direct product of indecomposable subgroups.DefinitionsWe say that a group G… …   Wikipedia