different between denomination vs subgroup

English

Etymology

From Middle English denominacion, from Old French denominacion, from Latin d?n?min?ti?.

Pronunciation

• (UK) IPA^(key): /d??n?m??ne???n/
• Rhymes: -e???n

Noun

denomination (countable and uncountable, plural denominations)

1. (uncountable) The act of naming or designating.
2. (countable) That by which anything is denominated or styled; an epithet; a name, designation, or title; especially, a general name indicating a class of like individuals
3. (countable, religion) A class, or society of individuals, called by the same name; a sect or religious subgroup.

   Hypernym: sect

   Hyponym: order
4. (countable) A unit in a series of units of weight, money, etc.

Derived terms

• denominational
• denominationalism

Related terms

• denominate

Translations

See also

• name
• appellation
• title
• face value

Further reading

• religious denomination on Wikipedia.Wikipedia
• denomination (currency) on Wikipedia.Wikipedia
• denomination in Webster’s Revised Unabridged Dictionary, G. & C. Merriam, 1913.
• denomination in The Century Dictionary, New York, N.Y.: The Century Co., 1911.

English

Etymology

sub- +? group.

Pronunciation

IPA^(key): /?s?b???u?p/

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

Translations

Verb

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

1. To divide or classify into subgroups