# Dominant group/Rigorous definition

What is a rigorous definition? And, specifically where dominant group is concerned, what is a rigorous definition of dominant group?
With dominant group appearing in almost every field of written human endeavor, especially primary sources, usually with what appears to be a relatively unique definition or usage, is a rigorous definition even possible?
Although primary sources are usually not read at a secondary education level, dominant group and some of its relative synonyms occur in secondary education resources such as Wikipedia.

## Dominant groups

Examples from primary sources are to be used to prove or disprove each hypothesis. These can be collected per subject or in general.
* Accident hypothesis: dominant group is an accident of whatever processes are operating.
* Artifact hypothesis: dominant group may be an artifact of human endeavor or may have preceded humanity.
* Association hypothesis: dominant group is associated in some way with the original research.
* Bad group hypothesis: dominant group is the group that engages in discrimination, abuse, punishment, and additional criminal activity against other groups. It often has an unfair advantage and uses it to express monopolistic practices.
* Control group hypothesis: there is a control group that can be used to study dominant group.
* Entity hypothesis: dominant group is an entity within each field where a primary author of original research uses the term.
* Evolution hypothesis: dominant group is a product of evolutionary processes, such groups are the evolutionary process, produce evolutionary processes, or are independent of evolutionary processes.
* Identifier hypothesis: dominant group is an identifier used by primary source authors of original research to identify an observation in the process of analysis.
* Importance hypothesis: dominant group signifies original research results that usually need to be explained by theory and interpretation of experiments.
* Indicator hypothesis: dominant group may be an indicator of something as yet not understood by the primary author of original research.
* Influence hypothesis: dominant group is included in a primary source article containing original research to indicate influence or an influential phenomenon.
* Interest hypothesis: dominant group is a theoretical entity used by scholarly authors of primary sources for phenomena of interest.
* Metadefinition hypothesis: all uses of dominant group by all primary source authors of original research are included in the metadefinition for dominant group.
* Null hypothesis: there is no significant or special meaning of dominant group in any sentence or figure caption in any refereed journal article.
* Object hypothesis: dominant group is an object within each field where a primary author of original research uses the term.
* Obvious hypothesis: the only meaning of dominant group is the one found in Mosby's Medical Dictionary.
* Original research hypothesis: dominant group is included in a primary source article by the author to indicate that the article contains original research.
* Primordial hypothesis: dominant group is a primordial concept inherent to humans such that every language or other form of communication no matter how old or whether extinct, on the verge of extinction, or not, has at least a synonym for dominant group.
* Purpose hypothesis: dominant group is written into articles by authors for a purpose.
* Regional hypothesis: dominant group, when it occurs, is only a manifestation of the limitations within a region. Variation of those limitations may result in the loss of a dominant group with the eventual appearance of a new one or none at all.
* Source hypothesis: dominant group is a source within each field where a primary author of original research uses the term.
* Term hypothesis: dominant group is a significant term that may require a 'rigorous definition' or application and verification of an empirical definition.

## Axiomatic definitions

A rigorous definition fulfills the axioms that define a definition so that a generalized definition can be defined using an appropriate function that fulfills the axioms. Having met these axioms as a criteria of a general definition, the definition is said to be a rigorous definition.
An axiomatic definition is a rigorous definition: "the definition must clearly state the rules that are considered as binding, and on the other hand give the implementor enough freedom to achieve efficiency by leaving certain less important aspects undefined."

## Synonyms

The term dominant group appears to be used to identify entities of importance. The genera differentia for possible relative synonyms of dominant group fall into the following set of orderable pairs:
Relative synonyms for dominant group :
| Synonym for "dominant" | Category Number | Category Title | Synonym for "group" | Category Number | Catgeory Title |
| “superior” | 36 | SUPERIORITY | "arrangement" | 60 | ARRANGEMENT |
| “influential” | 171 | INFLUENCE | "class" | 61 | CLASSIFICATION |
| “musical note” | 462 | HARMONICS | "assembly" | 74 | ASSEMBLAGE |
| “most important” | 670 | IMPORTANCE | "size" | 194 | SIZE |
| “governing” | 739 | GOVERNMENT | "painting", "grouping" | 572 | ART |
| "master" | 747 | MASTER | "association", "set" | 786 | ASSOCIATION |
| ----- | --- | ------- | "sect" | 1018 | RELIGIONS, CULTS, SECTS |
'Orderable' means that any synonym from within the first category can be ordered with any synonym from the second category to form an alternate term for dominant group; for example, "superior class", "influential sect", "master assembly", "most important group", and "dominant painting". "Dominant" falls into category 171. "Group" is in category 61. Further, any word which has its most or much more common usage within these categories may also form an alternate term, such as "ruling group", where "ruling" has its most common usage in category 739, or "dominant party", where "party" is in category 74. "Taxon" or "taxa" are like "species" in category 61. "Society" is in category 786 so there is a "dominant society".
When one or two orderable pairs are produced, the results are
* one pair - relative synonym,
* one pair in which the first or second category has each of two from a category - definition, and
* two pairs from two to four categories - definition.

## Meaningless dominant groups

Each subject area within which the term dominant group is used has the same problem: "unless and until a rigorous definition of the term 'dominant group' is rendered, the argument fails to establish its conclusion due to the fact that one of its premises is meaningless."

## Tests

Def. a category synonym for "group", including "group", and a category synonym for "dominant", including "dominant", that as one or two orderable pairs has only the properties of two pairs: i.e., from two to four categories [exclusive], or one pair in which the first or second category has up to each of two from a category is called a rigorous definition of dominant group.

## Hypotheses

* Dominant group has a rigorous metadefinition that accommodates all known primary source (original research) uses.