Subgroup

/ˈsʌbˌɡɹuːp/ · noun

Meaning

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

Definitions by Sense

1. A group within a larger group; a group whose members are some, but not all, of the members of a larger group.
2. (group theory) A subset H of a group G that is itself a group and has the same binary operation as G.
3. To divide or classify into subgroups

Example Sentences

1998, Robert A. Johnson, Prevalence of Substance Use Among Racial and Ethnic Subgroups in the United States, 1991-1993, Department of Health and Human Services, page B-11, Based on U.S. Bureau of the Census (1992c), other metropolitan areas that might be suitable for oversampling specific racial/ethnic subgroups include Miami (18% Cuban), New York City (7% Puerto Rican), Los Angeles (26% Mexican), and Honolulu (23% Japanese). Three techniques might be used to increase the yield of rare subgroup members within metropolitan areas where they are concentrated: 1) oversampling of areal segments containing high percentages of the subgroup, […] .

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.

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.

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.

Synonyms for subgroup

Antonyms for subgroup

Related Words

Word Forms

• subgroups
• subgrouping
• subgrouped

Usage Notes

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