On a group that acts freely on an Abelian group.
Mazurov, V.D., Churkin, V.A. (2001)
Sibirskij Matematicheskij Zhurnal
D. Dummit, J. Labute (1983)
Inventiones mathematicae
George S. Sacerdote (1972)
Mathematica Scandinavica
Viatcheslav N. Obraztsov (1998)
Rendiconti del Seminario Matematico della Università di Padova
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 , over the integers, is not -generated. This gives a negative answer to a question of M. Conder.
Martin D. Burrow, Arthur Steinberg (1989)
Compositio Mathematica
Albar, Muhammad A. (2000)
International Journal of Mathematics and Mathematical Sciences
Hilton, Peter, Militello, Robert (1996)
International Journal of Mathematics and Mathematical Sciences
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 is a free factor of a given free group . Known algorithms solve this problem in time polynomial in the sum of the lengths of the generators of and exponential in the rank of . We show that the latter dependency can be made exponential in the rank difference rank - rank, which often makes a significant change.
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.
Ivanov, Sergei V. (1998)
Electronic Research Announcements of the American Mathematical Society [electronic only]
Bell, G., Dranishnikov, A. (2001)
Algebraic & Geometric Topology
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.
Mikaelian, Vahagn H. (2004)
International Journal of Mathematics and Mathematical Sciences
Marc Conrad (2000)
Acta Arithmetica
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...
Veretennikov, B.M. (2007)
Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]
Bertram A.F. Wehrfritz (1980)
Mathematische Zeitschrift
Algebra i Logika
Mazurov, V. D. (2003)
Sibirskij Matematicheskij Zhurnal