This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "Polycyclic group" – news · newspapers · books · scholar · JSTOR(June 2008) (Learn how and when to remove this message)
Type of solvable group in mathematics
In mathematics, a polycyclic group is a solvable group that satisfies the maximal condition on subgroups (that is, every subgroup is finitely generated). Polycyclic groups are finitely presented, which makes them interesting from a computational point of view.
a polycyclicgroup is a solvable group that satisfies the maximal condition on subgroups (that is, every subgroup is finitely generated). Polycyclic groups...
trivial group. Every finitely generated abelian group or nilpotent group is polycyclic. Cycle graph (group) Cyclic module Cyclic sieving Prüfer group (countably...
contrast, for a solvable group the definition requires each quotient to be abelian. In another direction, a polycyclicgroup must have a subnormal series...
A polycyclic aromatic hydrocarbon (PAH) is a class of organic compounds that is composed of multiple aromatic rings. The simplest representative is naphthalene...
In the field of organic chemistry, a polycyclic compound is an organic compound featuring several closed rings of atoms, primarily carbon. These ring substructures...
contains free groups of infinite rank. Noetherian groups need not be finite extensions of polycyclicgroups. Infinite subgroup series can also be defined...
Saxitoxin Group. The EFSA Journal (2009) 1019, 1-76. Keith, Lawrence H. (2015-03-15). "The Source of U.S. EPA's Sixteen PAH Priority Pollutants". Polycyclic Aromatic...
G} is an extension of a Noetherian solvable group (i.e. a polycyclicgroup) by a finite group, then R [ G ] {\displaystyle R[G]} is two-sided Noetherian...
"Computing the Schur multiplicator and the nonabelian tensor square of a polycyclicgroup", Journal of Algebra, 320 (2): 927–944, doi:10.1016/j.jalgebra.2008...
polynomial rings, group algebras of polycyclicgroups, universal enveloping algebras of solvable Lie algebras, and coordinate rings of quantum groups. Suppose...
semigroups into groups, studied the isomorphism problem of group rings, established the Malçev correspondence for polycyclicgroups, and in the 1960s...
this pollution, by a lot of heavy metals and tar substances, so-called polycyclic hydrocarbons (PAHs), are moved from the fuel into the sea instead, and...
{\displaystyle G} . For example, polycyclicgroups have solvable word problems since the normal form of an arbitrary word in a polycyclic presentation is readily...
arrangement of classes of groups: cyclic < abelian < nilpotent < supersolvable < polycyclic < solvable < finitely generated group. A group G is called virtually...
Naphthalene is an organic compound with formula C 10H 8. It is the simplest polycyclic aromatic hydrocarbon, and is a white crystalline solid with a characteristic...
detergents led to its common use, which spurred further development of other polycyclic musks including Galaxolide. 3a,6,6,9a-Tetramethyldodecahydronaphtho-[2...
[better source needed] Most of the chemical compounds are polycyclic aromatic hydrocarbon: polycyclic aromatic hydrocarbons (4-rings: chrysene, fluoranthene...
finite groups. Examples of groups that are residually finite are finite groups, free groups, finitely generated nilpotent groups, polycyclic-by-finite...
Anthracene is a solid polycyclic aromatic hydrocarbon (PAH) of formula C14H10, consisting of three fused benzene rings. It is a component of coal tar....
Chlorinated polycyclic aromatic hydrocarbons (Cl-PAHs) are a group of compounds comprising polycyclic aromatic hydrocarbons with two or more aromatic...
more atoms. The term polycyclic is used when more than one ring appears in a single molecule. Naphthalene is formally a polycyclic compound, but is more...
finite group, by an elementary counting argument. More generally, every polycyclic-by-finite group. Any finitely generated free group. The additive group Q...
In formulas, the group is often abbreviated as Me. This hydrocarbon group occurs in many organic compounds. It is a very stable group in most molecules...
Complexes of Chromium with Alkynes. 2. Intramolecular Insertions Leading to Polycyclic Lactams". Journal of the American Chemical Society. 115 (23): 10568–10580...
Global Information