C standard library: Difference between revisions

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In [[mathematics]], the '''bimonster''' is a [[group (mathematics)|group]] that is the [[wreath product]] of the [[monster group]] ''M'' with '''Z'''<sub>2</sub>:
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:<math>Bi = M \wr \mathbb{Z}_2. \, </math>
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The Bimonster is also a quotient of the [[Coxeter group]] corresponding to the [[Dynkin diagram]] ''Y''<sub>555</sub>, a Y-shaped [[graph theory|graph]] with 16 nodes:
 
: {{Dynkin|nodes|3s|nodes|3s|nodes|3s|nodes|3s|branch1|node|3|node|3|node|3|node|3|node|3|node}}
 
[[File:BimonsterGroup.svg]]
 
[[John H. Conway]] [[conjecture]]d that a [[Presentation of a group|presentation]] of the bimonster could be given by adding a certain extra relation to the presentation defined by the ''Y''<sub>555</sub> diagram; this was proved in 1990 by [[A. A. Ivanov]] and [[Simon P. Norton]].
 
== See also ==
* [[Triality]] - [[simple Lie group]] D<sub>4</sub>, ''Y''<sub>111</sub>
 
== External links ==
* {{MathWorld | urlname=Bimonster | title=Bimonster}} (''Note: incorrectly named here as [3<sup>6,6,6</sup>]'')
 
[[Category:Group theory]]
 
 
{{Abstract-algebra-stub}}

Latest revision as of 01:05, 4 January 2015

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