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.

   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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   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, […] .

   Synonyms: subset

2. group theoryA subset H of a group G that is itself a group and has the same binary operation as G.

   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

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   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

   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

present singular third person subgroups · participle present subgrouping · participle past subgrouped · past subgrouped

1. To divide or classify into subgroups