Rudvalis group

Rudvalis group

In the mathematical field of group theory, the Rudvalis group "Ru" (found by .

Properties

The Rudvalis group act as a rank 3 permutation group on 4060 points, with one point stabilizer the Ree group 2"F"4(2), the automorphism group of the Tits group. This representation implies a strongly regular graph in which each vertex has 2304 neighbors and 1755 non-neighbors. Two adjacent vertices have 1328 common neighbors; two non-adjacent ones have 1208 Harvard citations|last=Griess|year=1998|loc=p. 125

Its Schur multiplier has order 2, and its outer automorphism group is trivial. Its double cover acts on a 28-dimensional lattice over the Gaussian integers. Reducing this lattice modulo the principal ideal

:(1 + "i")

gives an action of the Rudvalis group on a 28-dimensional vector space over the field with 2 elements. Duncan (2006) used this to construct a vertex operator algebra acted on by the double cover.

A novel simple subgroup of Ru is the Suzuki group Sz(8), order 21920, which is not divisible by 3. (Atlas of Finite Group Representations: Rudvalis group)

References

* Citation
last1 = Conway
first1 = J.H.
author1-link = John H. Conway
last2 = Wales
first2 = D.B.
title = The construction of the Rudvalis simple group of order 145926144000
journal = Journal of Algebra
issue = 27
year = 1973
pages = 538-548
* cite arXiv
author = John F. Duncan
title = Moonshine for Rudvalis's sporadic group
year = 2008
class = math.RT
version = v1
eprint = math/0609449
* Citation
last = Griess
first = R.L.
author-link = R. L. Griess
title = The Friendly Giant
journal = Inventiones Mathematicae
issue = 69
year = 1982
pages = 1-102
* Citation
last = Griess
first = R.L.
title = Twelve Sporadic Groups
year = 1998
publisher = Springer-Verlag
* Citation
last = Rudvalis
first = A.
author-link = Arunas Rudvalis
title = A new simple group of order 214 33 53 7 13 29
journal = Notices of the American Mathematical Society
issue = 20
year = 1973
pages = A-95

* [http://mathworld.wolfram.com/RudvalisGroup.html MathWorld: Rudvalis Group]
* [http://brauer.maths.qmul.ac.uk/Atlas/v3/spor/Ru/ Atlas of Finite Group Representations: Rudvalis group]


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