Subgroup

Quick meaning: Subgroup is a noun meaning A group within a larger group; a group whose members are some, but not all, of the members of a larger group.

Meaning

A group within a larger group; a group whose members are some, but not all, of the members of a larger group.

More Meanings

1. (group theory) A subset H of a group G that is itself a group and has the same binary operation as G.
2. To divide or classify into subgroups

Example Sentences

The most important application of dysprosium and terbium, which belong to a subgroup known as the heavy rare earths, is in devices called neodymium boron magnets, or neo magnets for short.

This is applied in Chapter 9 to prove the first congruence subgroup theorem, which asserts that g.z = z for all z in the center of the Drinfel'd double D(H) and all g in the principal congruence subgroup.

Much of the information about a group can be gleaned from a study of its subgroups. For these reasons it is important to study the subgroup structure of the almost simple groups, and in particular their maximal subgroups.

A subgroup H of an algebraic group G is called algebraic if H is an algebraic subvariety of G. Algebraic subgroups defined over k (as algebraic subvarieties) are called k-subgroups. An algebraic subgroup of an algebraic group is called k-closed or closed over k (resp. k-defined or defined over k) if it is k-closed (resp. k-defined) as an algebraic subvariety.

Word Forms

• subgroups
• subgrouping
• subgrouped

Synonyms for subgroup

Depending on context, synonyms include subset.

Related Words

Related dictionary entries include group, grouping, subclass, subcategory, subsector, clustering.

Related Dictionary Tools