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(2,3)-generation of the groups PSL6(q)

Tabakov, K., Tchakerian, K. (2011)

Serdica Mathematical Journal

2010 Mathematics Subject Classification: 20F05, 20D06.We prove that the group PSL6(q) is (2,3)-generated for any q. In fact, we provide explicit generators x and y of orders 2 and 3, respectively, for the group SL6(q).

A Garside presentation for Artin-Tits groups of type C ˜ n

F. Digne (2012)

Annales de l’institut Fourier

We prove that an Artin-Tits group of type C ˜ is the group of fractions of a Garside monoid, analogous to the known dual monoids associated with Artin-Tits groups of spherical type and obtained by the “generated group” method. This answers, in this particular case, a general question on Artin-Tits groups, gives a new presentation of an Artin-Tits group of type C ˜ , and has consequences for the word problem, the computation of some centralizers or the triviality of the center. A key point of the proof...

A new efficient presentation for P S L ( 2 , 5 ) and the structure of the groups G ( 3 , m , n )

Bilal Vatansever, David M. Gill, Nuran Eren (2000)

Czechoslovak Mathematical Journal

G ( 3 , m , n ) is the group presented by a , b a 5 = ( a b ) 2 = b m + 3 a - n b m a - n = 1 . In this paper, we study the structure of G ( 3 , m , n ) . We also give a new efficient presentation for the Projective Special Linear group P S L ( 2 , 5 ) and in particular we prove that P S L ( 2 , 5 ) is isomorphic to G ( 3 , m , n ) under certain conditions.

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