Definitions for subgroup
ˈsʌbˌgrupsub·group

Princeton's WordNetRate this definition:0.0 / 0 votes

1. subgroupnoun

   a distinct and often subordinate group within a group

2. subgroupnoun

   (mathematics) a subset (that is not empty) of a mathematical group

WiktionaryRate this definition:0.0 / 0 votes

1. subgroupnoun

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

2. subgroupnoun

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

3. subgroupverb

   To divide or classify into subgroups

WikipediaRate this definition:0.0 / 0 votes

1. Subgroup

   In group theory, a branch of mathematics, given a group G under a binary operation ∗, a subset H of G is called a subgroup of G if H also forms a group under the operation ∗. More precisely, H is a subgroup of G if the restriction of ∗ to H × H is a group operation on H. This is often denoted H ≤ G, read as "H is a subgroup of G". The trivial subgroup of any group is the subgroup {e} consisting of just the identity element.A proper subgroup of a group G is a subgroup H which is a proper subset of G (that is, H ≠ G). This is often represented notationally by H < G, read as "H is a proper subgroup of G". Some authors also exclude the trivial group from being proper (that is, H ≠ {e}).If H is a subgroup of G, then G is sometimes called an overgroup of H. The same definitions apply more generally when G is an arbitrary semigroup, but this article will only deal with subgroups of groups.

ChatGPTRate this definition:0.0 / 0 votes

1. subgroup

   A subgroup is a subset of a group that is itself a group under the operation of the larger group. The elements of a subgroup share a specific property, obey the group's laws, and the subgroup contains the group's identity element as well as the inverse of each element in the subgroup. In essence, it's a smaller group within a larger group that maintains the properties of group structure such as closure, associativity, identity and inverses.

Webster DictionaryRate this definition:0.0 / 0 votes

1. Subgroupnoun

   a subdivision of a group, as of animals

WikidataRate this definition:0.0 / 0 votes

1. Subgroup

   In mathematics, given a group G under a binary operation *, a subset H of G is called a subgroup of G if H also forms a group under the operation *. More precisely, H is a subgroup of G if the restriction of * to H x H is a group operation on H. This is usually represented notationally by H ≤ G, read as "H is a subgroup of G". A proper subgroup of a group G is a subgroup H which is a proper subset of G. The trivial subgroup of any group is the subgroup {e} consisting of just the identity element. If H is a subgroup of G, then G is sometimes called an overgroup of H. The same definitions apply more generally when G is an arbitrary semigroup, but this article will only deal with subgroups of groups. The group G is sometimes denoted by the ordered pair, usually to emphasize the operation * when G carries multiple algebraic or other structures. This article will write ab for a*b, as is usual.

Chambers 20th Century DictionaryRate this definition:0.0 / 0 votes

1. Subgroup

   sub′grōōp, n. any subordinate group in a classification.

Matched Categories

1. • Group
   • Math

How to pronounce subgroup?

1. Alex

   US English

   David

   US English

   Mark

   US English

   Daniel

   British

   Libby

   British

   Mia

   British

   Karen

   Australian

   Hayley

   Australian

   Natasha

   Australian

   Veena

   Indian

   Priya

   Indian

   Neerja

   Indian

   Zira

   US English

   Oliver

   British

   Wendy

   British

   Fred

   US English

   Tessa

   South African

How to say subgroup in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of subgroup in Chaldean Numerology is: 1

2. Pythagorean Numerology

   The numerical value of subgroup in Pythagorean Numerology is: 2

Examples of subgroup in a Sentence

1. Alessio Fasano:

   There is a possibility that some groups of individuals with other chronic inflammatory conditions, including autoimmune diseases like diabetes or multiple sclerosis, of course autism ... and schizophrenia ... there could be a subgroup of these individuals that could benefit from embracing a gluten-free diet, for schizophrenia, for example, we're talking about 20% or 25%. That's not a trivial number.

2. Barbara Carvalho:

   Those previous numbers cited were not of a full survey of Latinos but the result from the smaller subgroup that make up a survey of Americans. The margin of error was wide and the results should not be taken to conclude what would have been found among this very diverse group had we done a larger study of only Hispanic and Latino Americans.

3. Courtney Kennedy:

   There are a number of subgroup estimates that bounce around from poll to poll, as a result, the results are sometimes incoherent when looking across polls. This variation across polls is testament to the tremendous variation in the methods used to conduct polling these days.

4. Courtney Kennedy:

   I think poll watchers would do well to accept that the field is in an era of transition, and one consequence of that is a frustrating amount of noise in subgroup estimates.

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References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=subgroup
2. ^ Wiktionary
   https://en.wiktionary.org/wiki/Subgroup
3. ^ Wikipedia
   https://en.wikipedia.org/wiki/Subgroup
4. ^ ChatGPT
   https://chat.openai.com
5. ^ Webster Dictionary
   https://www.merriam-webster.com/dictionary/subgroup
6. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=subgroup
7. ^ Chambers 20th Century Dictionary
   https://www.gutenberg.org/files/37683/37683-h/37683-h.htm#:~:text=subgroup