Help:Definition lookup

For a complete list of all definitions, see Category:Terminology

''This page is intended for people using groupprops to read/learn definitions. Please also refer Groupprops:Definition for how to write definitions in Groupprops''

This page is intended to help people locate the definitions of what they're looking for. Further information is available at the pages on Category:Definition lookup pages.

Directly typing in the URL
If you know the name of the term, directly type in the URL. The URL for a term is given by:

where Termname is replaced by whatever the actual term name is.

Possible confusions:
 * Capitals versus smalls: The first letter is case-insensitive, but future letters are case-sensitive. Here, all term names are with further letters small, except the cases where we are using abbreviations. Thus, the page for normal subgroup has a small "s" for subgroup and reads as:


 * Hyphenation: In some cases, hyphenation has been used instead of spaces. For instance this is the policy when abbreviation prefixes are there, or when we are omitting a preposition. For instance, we say intersection-closed and not intersection closed for closed under intersections.

However, attempts have been made to provide redirects from the non-hyphenated versions to the hyphenated words.


 * British versus American spelling: Usually the page with one spelling has a redirect to the page with the other.

MediaWiki Search
To run a MediaWiki search for a term, you can type:

Or alternatively, in the search bar located in the left-hand column, type the search query.

If a page with the exact name (or a page with a redirect to the exact name) already exists, you will be redirected to the search page, otherwise, you will be shown a list of pages with matching titles and text.

Search using other search engines
You can also search for terms in Groupprops using external search engines like Google. Just type the name of the term in the Google search bar, followed by the words site:groupprops.subwiki.org

Lookup by categorization
In contrast to the search approach, is the approach of lookup using the categorical structure. Here, I describe some of the various aspects of the categorical structure that you can use.

All the subcategories can be accessed starting from Category:Terminology. This category can be accessed by clicking the Terms/definitions link in the sidebar, under the lookup header.

Organization by level and standardness
We have the following important subcategories:


 * Category:Standard terminology: This is terminology that is standard, and accepted, across the community. Some subcategories of interest:
 * Category:Basic definitions in group theory: These are definitions that are very basic to the subject.
 * Category:Semi-basic definitions in group theory
 * Category:Standard non-basic definitions in group theory


 * Category:Semistandard terminology: This is terminology that has appeared in a journal or published book but is not widely accepted as standard.
 * Category:Nonstandard terminology: This is terminology that is not standard. An importnat subcategory of this is Category:Terminology local to the wiki. To learn more about this, read about terminology local to the wiki.

Organization by topic

 * Category:Terminology related to specific disciplines lists terminology related to specific disciplines related to group theory. These categories can be extremely useful for narrowing one's search, and also for learning more about what kind of stuff is available on Groupprops.
 * Category:Terminology related to specific problems lists terminology related to specific problems in or related to group theory.

Property-theoretic organization
You can refer Category:Property-theoretic categories for a full list of categories designed on the property-theoretic paradigm. These categories include both term categories and fact categories. Some of the important term categories, and how to use them, are described below:


 * Property categories: This lists all categories which describe properties; by a property on a collection of objects is meant something which every object either satisfies or does not satisfy. For example, being a solvable group is a group property, and hence is listed in Category:Group properties; being an inner automorphism is an automorphism property, hence is listed in Category:Automorphism properties.

Some of the property categories have their own lookup pages, which describe how to look up pages within the category. For instance, Subgroup properties:Lookup is the lookup page for the category of subgroup properties. Please read these to get more of a flavor about property categories and how they're organized.


 * Metaproperty categories: This lists all categories which describe properties themselves evaluated over property spaces; for instance the notion of a transitive subgroup property is a subgroup metaproperty, and is hence listed in Category:Subgroup metaproperties.


 * Property modifier categories:


 * Property operator categories:


 * metametaproperty categories:

Attempts are being made to combine property-theoretic organization with the other methods of organization, to ensure faster lookup and easier exploration. These attempts are still in the infancy stage.

Variation and relationship
Another approach to definition lookup is to look at pages of terms that are closely related, in the hope of getting a link to the page that one wants; this may be particularly useful if one knows the definition of the term but not the term name.

Here are some approaches for this:


 * Look at pages which link to this page, and try to locate a link at the correct semantic location. For instance, if you are looking for a subgroup property that is stronger than the property of being a normal subgroup, look at the Stronger properties subsection in the article on normal subgroup. If you are looking for a group metaproperty that is satisfied by the group property of being solvable, look in the metaproperties section of the article on solvable group.
 * If this fails, use the What links here feature (in the toolbox in the left margin) to find out what pages link to a particular page. Backward links might work where forward links don't.
 * Use the relational category structure. For instance, Category:Variations of normality lists subgroup properties obtained by varying the property of normality while Category:Opposites of normality lists subgroup properties obtained as opposites to normality.

How the definition is written
Check out Groupprops:Definition for the format of the definition.

Cautionary points

 * Remember that material put up on Groupprops has not been thoroughly checked. Hence, take whatever is written here with a pinch of salt.
 * If you are also following a standard text or reference, try to reconcile the definition given here with the definition in the standard text or reference.
 * Beware of terminology local to the wiki. If the term being defined is itself local to the wiki, then please remember that this definition cannot be used outside without first defining the term.
 * Check if some of the terms used in the process of defining are local to the wiki. Sometimes, one of the many equivalent formulations used in the definition may use terminology local to the wiki.

What after mastering the definition?
Having mastered the definition, you can read the rest of the article. Remember, however, that many parts of the article may involve a whole lot of other concepts and ideas (some local to the wiki) that you may not currently be interested in.

To understand more about the structure and layout of a definition article, check out:

Groupprops:Definition article

Lookup strategies for particular kinds of terms
Different kinds of term definitions have different strategies for lookup and understanding. A full list of definition lookup pages is available at:

Category:Definition lookup pages