polycyclic group

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• 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

• Polycyclic — may refer to: * Polycyclic compound, in organic chemistry, a cyclic compound with more than one hydrocarbon loop or ring structures * Polycyclic group, in mathematics, a solvable group that satisfies the maximal condition on subgroups …   Wikipedia

• Polycyclic Aromatic Compounds —   Titre abrégé Polycycl. Aromat. Compd. Discipline Chimie organique …   Wikipédia en Français

• Polycyclic aromatic hydrocarbon — An illustration of typical polycyclic aromatic hydrocarbons. Clockwise from top left: benz(e)acephenanthrylene, pyrene and dibenz(ah)anthracene …   Wikipedia

• Supersolvable group — In mathematics, a group is supersolvable (or supersoluble) if it has an invariant normal series where all the factors are cyclic groups. Supersolvablility is stronger than the notion of solvability.DefinitionLet G be a group. G is supersolvable… …   Wikipedia

• M-group — In mathematics, especially in the field of group theory, the term M group may refer to a few distinct concepts: * monomial group, in character theory, a group whose complex irreducible characters are all monomial * Iwasawa group or modular group …   Wikipedia

• Chlorinated polycyclic aromatic hydrocarbon — Chlorinated polycyclic aromatic hydrocarbons (ClPAHs) are a group of compounds comprising polycyclic aromatic hydrocarbons with two or more aromatic rings and one or more chlorine atoms attached to the ring system. ClPAHs can be divided into two… …   Wikipedia

• Solvable group — Concepts in group theory category of groups subgroups, normal subgroups group homomorphisms, kernel, image, quotient direct product, direct sum semidirect product, wreath product …   Wikipedia

• History of group theory — The history of group theory, a mathematical domain studying groups in their various forms, has evolved in various parallel threads. There are three historical roots of group theory: the theory of algebraic equations, number theory and geometry.… …   Wikipedia

• Residually finite group — In the mathematical field of group theory, a group G is residually finite or finitely approximable if for every nontrivial element g in G there is a homomorphism h from G to a finite group, such that :h(g) eq 1.,There are a number of equivalent… …   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