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On a question of M. Conder

M. Chiara Tamburini, Paola Zucca (2000)

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

We show that the special linear group S L 3 , Z , over the integers, is not 2 , 3 -generated. This gives a negative answer to a question of M. Conder.

On an algorithm to decide whether a free group is a free factor of another

Pedro V. Silva, Pascal Weil (2008)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We revisit the problem of deciding whether a finitely generated subgroup H is a free factor of a given free group F . Known algorithms solve this problem in time polynomial in the sum of the lengths of the generators of H and exponential in the rank of F . We show that the latter dependency can be made exponential in the rank difference rank ( F ) - rank ( H ) , which often makes a significant change.

On an algorithm to decide whether a free group is a free factor of another

Pedro V. Silva, Pascal Weil (2007)

RAIRO - Theoretical Informatics and Applications

We revisit the problem of deciding whether a finitely generated subgroup H is a free factor of a given free group F. Known algorithms solve this problem in time polynomial in the sum of the lengths of the generators of H and exponential in the rank of F. We show that the latter dependency can be made exponential in the rank difference rank(F) - rank(H), which often makes a significant change.

On centrally nilpotent loops

L. V. Safonova, K. K. Shchukin (2000)

Commentationes Mathematicae Universitatis Carolinae

Using a lemma on subnormal subgroups, the problem of nilpotency of multiplication groups and inner permutation groups of centrally nilpotent loops is discussed.

On exponential growth rates for free groups.

Malik Koubi (1998)

Publicacions Matemàtiques

Let Fp be a free group of rank p ≥ 2. It is well-known that, with respect to a p-element generating set, that is, a basis, the exponential growth rate of Fp is 2p-1. We show that the exponential growth rate τ of a group G with respect to a p-element generating set X is 2p-1 if and only if G is free on X; otherwise τ < 2p-1. We also prove that, for any finite generating set X of Fp which is disjoint from X-1, the exponential growth rate τ of Fp with respect to X is 2p-1 if and only if X is...

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