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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.

A note on a class of factorized p -groups

Enrico Jabara (2005)

Czechoslovak Mathematical Journal

In this note we study finite p -groups G = A B admitting a factorization by an Abelian subgroup A and a subgroup B . As a consequence of our results we prove that if B contains an Abelian subgroup of index p n - 1 then G has derived length at most 2 n .

A note on loops of square-free order

Emma Leppälä, Markku Niemenmaa (2013)

Commentationes Mathematicae Universitatis Carolinae

Let Q be a loop such that | Q | is square-free and the inner mapping group I ( Q ) is nilpotent. We show that Q is centrally nilpotent of class at most two.

A note on the minimal normal Fitting class

Marco Barlotti (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Un gruppo finito ciclico-per-nilpotente appartiene alla minima classe di Fitting normale se e solo se è nilpotente.

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