FiniteGroupCount
gives the number of finite groups of order n.
Details
- Integer mathematical function, suitable for both symbolic and numerical manipulation.
- FiniteGroupCount automatically threads over lists.
Examples
open all close allBasic Examples (2)
Table[FiniteGroupCount[n], {n, 20}]Use FiniteGroupCount to plot the number of finite groups of small order:
DiscretePlot[FiniteGroupCount[n], {n, 1, 20}]Scope (2)
FiniteGroupCount[2 3 5 7 11]FiniteGroupCount threads element-wise over lists:
FiniteGroupCount[{2, 3, 4}]Applications (2)
Density of 1 for groups with order less than 
:
Count[FiniteGroupCount[Range[10 ^ 4]], 1] / 10. ^ 4ListLinePlot[Table[Count[FiniteGroupCount[Range[2 ^ n]], 1] / 2. ^ n, {n, 13}]]The number of non-Abelian groups of order n:
Table[FiniteGroupCount[n] - FiniteAbelianGroupCount[n], {n, 20}]Properties & Relations (2)
FiniteGroupCount[p] takes the value 1 for all prime p:
Table[FiniteGroupCount[Prime[n]], {n, 10}]FiniteGroupCount[p^2] takes the value 2 for all prime p:
Table[FiniteGroupCount[Prime[n] ^ 2], {n, 10}]FiniteGroupCount[p^3] takes the value 5 for all prime p:
Table[FiniteGroupCount[Prime[n] ^ 3], {n, 10}]FindSequenceFunction can recognize the FiniteGroupCount sequence:
Table[FiniteGroupCount[n], {n, 10}]FindSequenceFunction[%, n]Text
Wolfram Research (2008), FiniteGroupCount, Wolfram Language function, https://reference.wolfram.com/language/ref/FiniteGroupCount.html.
CMS
Wolfram Language. 2008. "FiniteGroupCount." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/FiniteGroupCount.html.
APA
Wolfram Language. (2008). FiniteGroupCount. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FiniteGroupCount.html