Property talk:P1164

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group cardinality
number of elements in a finite group in mathematics

Description	The number of elements in a finite group
Represents	group order (Q18408315)
Data type	Quantity
Domain	According to this template: finite group (Q1057968) According to statements in the property: finite group (Q1057968) When possible, data should only be stored as statements
Allowed values	According to this template: positive integers According to statements in the property: 0 ≤ 𝓧 ≤ not applicable When possible, data should only be stored as statements
Allowed units	not applicable
Example	dihedral group of order 6 (Q2204630) → 6 Klein four-group (Q550593) → 4 Mathieu group M11 (Q6787235) → 7,920 Conway group Co3 (Q5166742) → 495,766,656,000
Source	e.g. w:List of small groups and w:List of finite simple groups (note: this information should be moved to a property statement; use property source website for the property (P1896))
Tracking: usage	Category:Pages using Wikidata property P1164 (Q56178456)
See also	cardinality of this set (P2820)
Lists	Items with the most statements of this property Count of items by number of statements (chart) Items with the most statements Items with the fewest statements Count of items by number of sitelinks (chart) Items with the most sitelinks Items with the most sitelinks, but no link to one Wikipedia (sample: Welsh Wikipedia, cywiki) Items with the fewest sitelinks Most linked wikis Items with the most identifier properties Items with no other statements Most recently created items Items with novalue claims Items with unknown value claims Usage history (total) Usage history (main statement) Minimum and maximum Items with highest numeric value Items with lowest numeric value User:Laboramus/Units/P1164 (Units used) Database reports/Constraint violations/P1164 Map Random list
Proposal discussion	Proposal discussion
Current uses	Total 50 Main statement 46 92% of uses Qualifier 4 8% of uses

[create Create a translatable help page (preferably in English) for this property to be included here]

Range from “0” to “+∞”: values should be in the range from “0” to “+∞”. (Help)

Exceptions are possible as rare values may exist. Exceptions can be specified using exception to constraint (P2303).
List of violations of this constraint: Database reports/Constraint violations/P1164#Range

Type “finite group (Q1057968)”: item must contain property “instance of (P31)” with classes “finite group (Q1057968)” or their subclasses (defined using subclass of (P279)). (Help)

Exceptions are possible as rare values may exist. Exceptions can be specified using exception to constraint (P2303).
List of violations of this constraint: Database reports/Constraint violations/P1164#Type Q1057968, SPARQL

No bounds: values can't have any bounds (e.g. 1 not 1±0) (Help)

Exceptions are possible as rare values may exist. Exceptions can be specified using exception to constraint (P2303).
List of violations of this constraint: Database reports/Constraint violations/P1164#No Bounds, SPARQL

Units: “novalue”: value unit must be one of listed. (Help)

Exceptions are possible as rare values may exist. Exceptions can be specified using exception to constraint (P2303).
List of violations of this constraint: Database reports/Constraint violations/P1164#Units

Integer: values should be integers (ie. they shouldn't have a fractional part) (Help)

Exceptions are possible as rare values may exist. Exceptions can be specified using exception to constraint (P2303).
List of violations of this constraint: Database reports/Constraint violations/P1164#integer, SPARQL

Scope is as main value (Q54828448): the property must be used by specified way only (Help)

List of violations of this constraint: Database reports/Constraint violations/P1164#Scope, hourly updated report, SPARQL

Allowed entity types are Wikibase item (Q29934200): the property may only be used on a certain entity type (Help)

Exceptions are possible as rare values may exist. Exceptions can be specified using exception to constraint (P2303).
List of violations of this constraint: Database reports/Constraint violations/P1164#Entity types

Increased range

I increased the range of values to include the cardinality of the monster group (Q392663). If anybody objects, they can revert the change and instead add Q392663 as an exception. The-erinaceous-one (talk) 04:20, 15 September 2020 (UTC)

• I revised my edit to "no value" because there really is no upper limit on the size of a group. The-erinaceous-one (talk) 07:11, 16 September 2020 (UTC)

What about redoing this with data type item?

I think cardinality statements here in Wikidata could be more more useful if they were expressed with items as values, where those items would then have a statement about numeric value (P1181), plus potentially other statements, e.g. for prime factor (P5236). So I would think that we should look into having a new cardinality property (let's call it $P^{*}$ for now) that would have an item as its value, e.g. monster group (Q392663): $P^{*}$ = 808017424794512875886459904961710757005754368000000000 (Q98609672). Before proposing such a new property, I wanted to check what people here think about such a change. --Daniel Mietchen (talk) 23:11, 28 October 2020 (UTC)

Opensofias
Tobias1984
Arthur Rubin
Cuvwb
TomT0m
Physikerwelt
Lymantria
Bigbossfarin
Infovarius
Helder
PhilMINT
Malore
Lore.mazza51
Wikisaurus
The Anome
The-erinaceous-one
Daniel Mietchen
Haansn08
Xenmorpha
John Samuel
Jeremy Dover
Toni 001
Bocardodarapti
Duckmather
HTinC23
fgnievinski

Notified participants of WikiProject Mathematics. --Daniel Mietchen (talk) 23:13, 28 October 2020 (UTC)

@Daniel Mietchen: The usefulness of the item datatype could be to generalize the property to infinite cardinalities, I think, not for finite cardinalities. If it’s just for finite cardinalities, we could in sparql for example do a join with the numeric value to retrieve the corresponding number item :

select ?group ?num_item ?num_value where {
  ?group wdt:P1164 ?num_value . 
  optional { 
    ?num_item wdt:P1181 ?num_value . 
    ?num_item wdt:P31 wd:Q21199 . 
  }
}

Try it!

Of course this depends on which usecase you have in mind as such a join is not possible in Wikipedia lua modules atm. author  TomT0m / talk page 08:39, 29 October 2020 (UTC)

We already have cardinality of this set (P2820). Is that what you are looking for? — The Erinaceous One 🦔 19:53, 29 October 2020 (UTC)