subgroup en · NOUN
Pronunciation
- /ˈsʌbˌɡɹuːp/
- (US) audio
Etymology
From sub- + group.
Meanings
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A group within a larger group; a group whose members are some, but not all, of the members of a larger group.
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.
2025 July 18, Timothy McLaughlin, “A Rebel Army Is Building a Rare-Earth Empire on China's Border. The Kachin Independence Organization fought for decades in obscurity. Now it's supplying essential minerals to manufacturers around the world”, in Bloomberg Businessweek, archived from the original on 18 Jul 2025:
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A subset H of a group G that is itself a group and has the same binary operation as G.
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.
1990, Peter B. Kleidman, Martin W. Liebeck, The Subgroup Structure of the Finite Classical Groups, Cambridge University Press, page 1: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.
2012, Yorck Sommerhäuser, Yongchang Zhu, Hopf Algebras and Congruence Subgroups, American Mathematical Society, page 3: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.
1991, Gregori A. Margulis, Discrete Subgroups of Semisimple Lie Groups, Springer-Verlag, page 13:
Forms
| Spelling | Features | Labels | Source |
|---|---|---|---|
| subgroups | Number=Plur | lexicographic |
Deriveds
stabilizer subgroup · trivial subgroup · subsubgroup · subgroupiness · stable subgroup · proper subgroup · torsion subgroup · commutator subgroup · intrasubgroup · Cartan subgroup · intersubgroup · derived subgroup · Fitting subgroup · normal subgroup
Synonyms
subset (group within a group)
Translations (48)
cmn 子群 ((group theory) group within a larger group) · bg по́дгрупа (group within a larger group) · sh подгрупа (group within a larger group) · fi aliryhmä (group within a larger group) · ro subgrup ((group theory) group within a larger group) · pl podgrupa ((group theory) group within a larger group) · fr sous-groupe ((group theory) group within a larger group) · ja 亜群 (group within a larger group) · ca subgrup ((group theory) group within a larger group) · gl subgrupo ((group theory) group within a larger group) · cmn 亞群 /亚群 (group within a larger group) · de Untergruppe ((group theory) group within a larger group) · es subgrupo ((group theory) group within a larger group) · pt subgrupo ((group theory) group within a larger group) · es subgrupo (group within a larger group) · cmn 子群 (group within a larger group) · ga foghrúpa (group within a larger group) · de Untergruppe (group within a larger group) · tr altöbek (group within a larger group) · cs podgrupa ((group theory) group within a larger group) · sv undergrupp (group within a larger group) · is undirflokkur (group within a larger group) · it sottogruppo (group within a larger group) · tr altküme ((group theory) group within a larger group) · fr sous-groupe (group within a larger group) · hu részcsoport ((group theory) group within a larger group) · is hlutgrúpa ((group theory) group within a larger group) · tr alttakım (group within a larger group) · ru подгру́ппа (group within a larger group) · ru подгру́ппа ((group theory) group within a larger group) · sh podgrupa ((group theory) group within a larger group) · fi aliryhmä ((group theory) group within a larger group) · sv delgrupp ((group theory) group within a larger group) · tr alt -grup (group within a larger group) · nb undergruppe (group within a larger group) · ro subgrup (group within a larger group) · nn undergruppe (group within a larger group) · sh podgrupa (group within a larger group) · ga foghrúpa ((group theory) group within a larger group) · ja 部分群 (group within a larger group) · fa زیرگروه (group within a larger group) · gl subgrupo (group within a larger group) · sk podgrupa ((group theory) group within a larger group) · pt subgrupo (group within a larger group) · pl podgrupa (group within a larger group) · it sottogruppo ((group theory) group within a larger group) · cs podskupina (group within a larger group) · ca subgrup (group within a larger group)