Groupprops:Definition article-tagging templates

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There is significant overlap between content in this article and content in the article Groupprops:Organizational principles, although the latter focusses on the principles while this focusses more on the implementation

Article-tagging templates are used in groupprops to tag entire articles. Article-tagging templates are typically put right at the top of the article, and may include:

  • A short description of the type of term/fact the article is about
  • A description of the level of difficulty and standardness of the terminology
  • A link to other articles of the same type, or of a contrasting type
  • Inclusion in a relevant category

Usually, the template renders output in a boxed quotation, right on top of the page.

The purpose of having templates is to provide a standard way, across pages, of describing the nature of a page, right on top, and also to give quick and easy access to other related ideas. Templates are the local tool to implementing a number of different organizational paradigms on this wiki, and help users understand these paradigms through self-exploration.

This page gives a summary of the templates, what parameters they take, and when they should be used. To learn more about the template, click on the relevant template.

Templates indicating difficulty, standardness and discipline

For every definition article, there should be exactly one such template in use, and it should be right at the top of the page (a number of articles do not use such a template, and this is being corrected).

For standard terminology in group theory

The following templates have emerged for standard terminology:

  • Template:Basicdef which is used for basic definitions that are common knowledge to most people who have done a first course in group theory.
  • Template:Semibasicdef which is placed slightly higher than basic definitions, in the sense that it includes terminology that may not be covered in a first course.
  • Template:Stdnonbasicdef which is placed even higher, in the sense that it includes terms that people outside the subject may not be well aware of, even though it may be standard within the subject.

For instance, the basic definition template comes right at the top of the page, and says:

This article is about a basic definition in group theory. The article text may, however, contain more material. Rate its utility as a basic definition article on the talk page

View a complete list of basic definitions in group theory OR Go through a guided tour for beginners to this wiki

For seminstandard terminology in group theory

Template:Semistddef is used for semistandard definitions.

For nonstandard terminology in group theory

  • Template:Nonstandard refers to general nonstandard terminology (that may be somewhat in use outside the wiki)

For terminology in other areas

For terminology local to the wiki

Property-theoretic type templates

Property space specification templates

A property space specification template is used when the term being defined is a property, viz a member of some property space. For instance, the term characteristic subgroup describes a subgroup property, and hence is an element of the subgroup property space. Hence, it is tagged with the Template:Subgroup property label.

A list of property space specification templates is available at:

Category: Property space specification templates

This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof.
View a complete list of subgroup properties

Metaproperty space specification templates

A metaproperty space specification template is used when the term being defined is a property over properties. For instance, the term transitive subgroup property is defined as follows: A subgroup property p is termed transitive if, whenever G satisfies p as a subgroup of H, and H satisfies the property as a subgroup of K, then G satisfies p as a subgroup of K.

This is a property that can be evaluated for any subgroup property. Hence it is a subgroup metaproperty.

A list of metaproperty space specification templates is available at:

Category: Metaproperty space specification templates

For instance, the template for a subgroup metaproperty looks like:

This article defines a subgroup metaproperty: a property that can be evaluated to true/false for any subgroup property

View a complete list of subgroup metaproperties

Operator-type specification templates

Some terms may be for property modifiers, property operators or more general operators. For instance the left transiter is an operator that takes as input a subgroup property and outputs a subgroup property. Ths, it can be classified as a subgroup property modifier, because it modifies an existing subgroup property.

A list of all the operator-type specification templates is available at:

Category: Operator-type specification templates

Other property-theoretic specification templates

A complete listing of property-theoretic specification template types is available at:

Category: Property-theoretic specification template types

Relational templates

Is-of templates

These are templates which say something like : this term is a variation/opposite/instance of something. For instance, the property of being a pronormal subgroup is a variation of the property of being a normal subgroup. Hence, we say that the property of being pronormal is a variation of the property of being normal. This is done using Template:Variationof which, in addition to printing a message on top, also includes the property in the relevant variational category. It also gives links to other variations on the same theme, and links to a survey article describing variations on that theme.

Similarly, we have Template:Oppositeof to indicate oppositeness to something.

Another very useful template is Template:Analogue in-of. This indicates that the term being defined, is an analogue, in something else, of another term, that may be more standard or more famous. This template causes inclusion in two categories, and links to other articles in both categories are given.

General term templates

The Template:Particularcases says that the article we've stumbled upon is a general term, and particular cases (instances) are available in a category listing; a link to the category listing is provided. This does not cause inclusion in any category.