Geodesic
A 2-generated 2-related group with no non-trivial finite quotients
Algebra and discrete mathematics, no. 2 (2007), pp. 111-114 
A. Yu. Ol'shanskii; M. V. Sapir. A 2-generated 2-related group with no non-trivial finite quotients. Algebra and discrete mathematics, no. 2 (2007), pp. 111-114. http://geodesic.mathdoc.fr/item/ADM_2007_2_a9/
@article{ADM_2007_2_a9,
     author = {A. Yu. Ol'shanskii and M. V. Sapir},
     title = {A 2-generated 2-related group with no non-trivial finite quotients},
     journal = {Algebra and discrete mathematics},
     pages = {111--114},
     year = {2007},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2007_2_a9/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We construct a 2-generated 2-related group without non-trivial finite factors-groups. This answers a question of J. Button.