subgroup

English

Etymology

From sub- +‎ group.

Pronunciation

IPA^(key): /ˈsʌbˌɡɹuːp/

Noun

subgroup (plural subgroups)

1. 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, […] .

2. (group theory) A subset H of a group G that is itself a group and has the same binary operation as G.
   • 1990, Peter B. Kleidman, Martin W. Liebeck, The Subgroup Structure of the Finite Classical Groups, Cambridge University Press, page 1:

     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.

   • 1991, Gregori A. Margulis, Discrete Subgroups of Semisimple Lie Groups, Springer-Verlag, page 13:

     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.

   • 2012, Yorck Sommerhäuser, Yongchang Zhu, Hopf Algebras and Congruence Subgroups, American Mathematical Society, page 3:

     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

• (group within a group): subset

Derived terms

• Cartan subgroup
• commutator subgroup
• derived subgroup
• Fitting subgroup
• normal subgroup
• proper subgroup
• stabilizer subgroup
• stable subgroup
• subgroupiness
• subsubgroup
• torsion subgroup
• trivial subgroup

 

Translations

group within a larger group

• Bulgarian: по́дгрупа f (pódgrupa)
• Catalan: subgrup m
• Chinese:

  Mandarin: 子群 (zh) (zǐqún), 亞群／亚群 (yàqún)

• Czech: podskupina f
• Finnish: aliryhmä
• French: sous-groupe (fr) f
• Galician: subgrupo m
• German: Untergruppe (de) f
• Icelandic: undirflokkur m
• Irish: foghrúpa m
• Italian: sottogruppo
• Japanese: 部分群 (ぶぶんぐん, bubungun), 亜群 (あぐん, agun)
• Norwegian:

  Bokmål: undergruppe m or f

  Nynorsk: undergruppe f

• Persian: زیرگروه (fa) (zirgoruh)
• Polish: podgrupa f
• Portuguese: subgrupo (pt) m
• Romanian: subgrup n
• Russian: подгру́ппа (ru) f (podgrúppa)
• Serbo-Croatian: podgrupa (sh) f, подгрупа f
• Spanish: subgrupo (es)
• Swedish: undergrupp (sv) c
• Turkish: alt -grup, altöbek, alttakım

(group theory) group within a larger group

• Catalan: subgrup m
• Czech: podgrupa (cs) f
• Finnish: aliryhmä
• French: sous-groupe (fr) m
• Galician: subgrupo m
• German: Untergruppe (de) f
• Hungarian: részcsoport (hu)
• Icelandic: hlutgrúpa f
• Irish: foghrúpa m
• Italian: sottogruppo m
• Portuguese: subgrupo (pt) m
• Romanian: subgrup n
• Russian: подгру́ппа (ru) f (podgrúppa)
• Serbo-Croatian: podgrupa (sh) f
• Slovak: podgrupa f
• Spanish: subgrupo (es) m
• Swedish: delgrupp (sv) c
• Turkish: altküme (tr)

Verb

subgroup (third-person singular simple present subgroups, present participle subgrouping, simple past and past participle subgrouped)

1. To divide or classify into subgroups