TitsGroupT
TitsGroupT
represents the simple Tits group 
.
Details
- The default permutation representation of TitsGroupT[] acts on points {1,…,1600}.
Background & Context
- TitsGroupT[] represents the Tits group
, sometimes also denoted 
, which is a group of order ![TemplateBox[{2, 11}, Superscript].TemplateBox[{3, 3}, Superscript].TemplateBox[{5, 2}, Superscript].13](Files/TitsGroupT.en/4.png "TemplateBox[{2, 11}, Superscript].TemplateBox[{3, 3}, Superscript].TemplateBox[{5, 2}, Superscript].13")
. The default representation of TitsGroupT is as a permutation group on the symbols 
having two generators. - The Tits group was first introduced in the mid-1960s by mathematician Jacques Tits as the (simple) derived subgroup of the (non-simple) Ree group
of Lie type. Because 
is not strictly a group of Lie type, it is sometimes regarded as a 27
sporadic simple group. The Tits group can be realized as a maximal subgroup of the Fischer group 
. In addition to its default permutation representation, it can be defined in terms of generators and relations as 
, where 
. - The usual group theoretic functions may be applied to TitsGroupT[], including GroupOrder, GroupGenerators, GroupElements and so on. A number of precomputed properties of the Tits group are available via FiniteGroupData["Tits","prop"].
- When considered together with the "true" sporadic finite simple groups, TitsGroupT[] is considered a "pariah" even though it occurs as a subquotient of MonsterGroupM (which is the criterion whose failure makes JankoGroupJ1, JankoGroupJ3, JankoGroupJ4, LyonsGroupLy, ONanGroupON and RudvalisGroupRu "pariahs").
Examples
Basic Examples (3)
TitsGroupT[]//GroupOrderNumber of points moved by the generators of a permutation representation of the Tits group:
Map[PermutationLength, TitsGroupT[]//GroupGenerators]Order of a pseudorandom element of the group:
SeedRandom[100];
RandomPermutation[TitsGroupT[]]//PermutationOrder
Wolfram Research (2010), TitsGroupT, Wolfram Language function, https://reference.wolfram.com/language/ref/TitsGroupT.html.
Text
Wolfram Research (2010), TitsGroupT, Wolfram Language function, https://reference.wolfram.com/language/ref/TitsGroupT.html.
CMS
Wolfram Language. 2010. "TitsGroupT." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/TitsGroupT.html.
APA
Wolfram Language. (2010). TitsGroupT. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/TitsGroupT.html