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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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