Group vs. Semigroup

Groupnoun

A number of things or persons being in some relation to one another.

Groupnoun

(group theory) A set with an associative binary operation, under which there exists an identity element, and such that each element has an inverse.

Groupnoun

An effective divisor on a curve.

Groupnoun

A (usually small) group of people who perform music together.

Groupnoun

(astronomy) A small number (up to about fifty) of galaxies that are near each other.

Groupnoun

(chemistry) A column in the periodic table of chemical elements.

Groupnoun

(chemistry) A functional group.

Groupnoun

(sociology) A subset of a culture or of a society.

Groupnoun

(military) An air force formation.

Groupnoun

(geology) A collection of formations or rock strata.

Groupnoun

(computing) A number of users with same rights with respect to accession, modification, and execution of files, computers and peripherals.

Groupnoun

An element of an espresso machine from which hot water pours into the portafilter.

Groupnoun

(music) A number of eighth, sixteenth, etc., notes joined at the stems; sometimes rather indefinitely applied to any ornament made up of a few short notes.

Groupnoun

(sports) A set of teams playing each other in the same division, while not during the same period playing any teams that belong to other sets in the division.

Groupnoun

(business) A commercial organization.

Groupverb

(transitive) To put together to form a group.

Groupverb

(intransitive) To come together to form a group.

Groupnoun

A cluster, crowd, or throng; an assemblage, either of persons or things, collected without any regular form or arrangement; as, a group of men or of trees; a group of isles.

Groupnoun

An assemblage of objects in a certain order or relation, or having some resemblance or common characteristic; as, groups of strata.

Groupnoun

A variously limited assemblage of animals or plants, having some resemblance, or common characteristics in form or structure. The term has different uses, and may be made to include certain species of a genus, or a whole genus, or certain genera, or even several orders.

Groupnoun

A number of eighth, sixteenth, etc., notes joined at the stems; - sometimes rather indefinitely applied to any ornament made up of a few short notes.

Groupverb

To form a group of; to arrange or combine in a group or in groups, often with reference to mutual relation and the best effect; to form an assemblage of.

Groupnoun

any number of entities (members) considered as a unit

Groupnoun

(chemistry) two or more atoms bound together as a single unit and forming part of a molecule

Groupnoun

a set that is closed, associative, has an identity element and every element has an inverse

Groupverb

arrange into a group or groups;

Groupverb

form a group or group together

Semigroupnoun

(mathematics) Any set for which there is a binary operation that is closed and associative.

Semigroup

In mathematics, a semigroup is an algebraic structure consisting of a set together with an associative binary operation. The binary operation of a semigroup is most often denoted multiplicatively: x·y, or simply xy, denotes the result of applying the semigroup operation to the ordered pair (x, y).