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A locally cyclic group is a group in which each finitely generated subgroup is cyclic. An example is the additive group of the rational numbers: every finite set of rational numbers is a set of integer multiples of a single unit fraction, the inverse of their lowest common denominator, and generates as a subgroup a cyclic group of integer ...
The subgroup of order n / d is a subgroup of the subgroup of order n / e if and only if e is a divisor of d. The lattice of subgroups of the infinite cyclic group can be described in the same way, as the dual of the divisibility lattice of all positive integers. If the infinite cyclic group is represented as the additive group on the integers ...
Cyclic compounds may or may not exhibit aromaticity; benzene is an example of an aromatic cyclic compound, while cyclohexane is non-aromatic. In organic chemistry, the term aromaticity is used to describe a cyclic (ring-shaped), planar (flat) molecule that exhibits unusual stability as compared to other geometric or connective arrangements of ...
Heterocyclic compound. A heterocyclic compound or ring structure is a cyclic compound that has atoms of at least two different elements as members of its ring (s). [1] Heterocyclic organic chemistry is the branch of organic chemistry dealing with the synthesis, properties, and applications of organic heterocycles. [2]
The monogenic semigroup generated by the singleton set {a} is denoted by . The set of elements of is {a, a2, a3, ...}. There are two possibilities for the monogenic semigroup : am = an ⇒ m = n. In the former case is isomorphic to the semigroup ( {1, 2, ...}, +) of natural numbers under addition. In such a case, is an infinite monogenic ...
In applied mathematics, finite subgroups of SU (2) are groups composed of rotations and related transformations, employed particularly in the field of physical chemistry. The symmetry group of a physical body generally contains a subgroup (typically finite) of the 3D rotation group. It may occur that the group {±1} with two elements acts also ...
The skeletal formula of acetamidine (acetimidamide). Amidines are organic compounds with the functional group RC(NR)NR 2, where the R groups can be the same or different. They are the imine derivatives of amides (RC(O)NR 2). The simplest amidine is formamidine, HC(=NH)NH 2. Examples of amidines include: DBU; diminazene; benzamidine; Pentamidine ...
A group that is generated by a single element is called cyclic. Every infinite cyclic group is isomorphic to the additive group of the integers Z. A locally cyclic group is a group in which every finitely generated subgroup is cyclic. The free group on a finite set is finitely generated by the elements of that set .