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

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