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Constructing a Representation of the Group (2, 3, 7; 11)

✍ Scribed by D.F. HOLT; W. PLESKEN; B. SOUVIGNIER

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
287 KB
Volume
24
Category
Article
ISSN
0747-7171

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✦ Synopsis

We construct a representation of the finitely presented group G := x, y | x 2 , y 3 , (xy) 7 , [x, y] 11 . This is done by lifting a representation over a finite field to a sufficently large quotient of local field and by finding minimal polynomials for the entries of this representation. We finally obtain a 7-dimensional representation over an algebraic number field K of degree 10 over the rationals, providing a homomorphism of G into a Lie group of type G 2 over K.

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