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AUTOMORPHISM GROUPS OF FREE GROUPS

Published online by Cambridge University Press:  01 December 2008

M. F. NEWMAN*
Affiliation:
Mathematical Sciences Institute, Australian National University, ACT 0200, Australia (email: [email protected])
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Abstract

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This note contains some remarks on generating pairs for automorphism groups of free groups. There has been significant use of electronic assistance. Little of this is used to verify the results.

MSC classification

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2009

References

[1]Armstrong, H., Forrest, B. and Vogtmann, K., ‘A presentation for Aut(F n)’, J. Group Theory 11(2) (2008), 267276.CrossRefGoogle Scholar
[2]Bosma, W., Cannon, J. and Playoust, C., ‘The Magma algebra system. I. The user language’, J. Symbolic Comput. 24(3–4) (1997), 235265 (Computational Algebra and Number Theory, London, 1993).Google Scholar
[3]Bray, J. N., Conder, M. D. E., Leedham-Green, C. R. and O’Brien, E. A., ‘Short presentations for alternating and symmetric groups’, Preprint, 2008.Google Scholar
[4]Chandler, B. and Magnus, W., The History of Combinatorial Group Theory, Studies in the History of Mathematics and Physical Sciences, 9 (Springer, New York, 1982).Google Scholar
[5]Coxeter, H. S. M. and Moser, W. O. J., Generators and Relations for Discrete Groups, 4th edn, Ergebnisse der Mathematik und ihrer Grenzgebiete, 14 (Springer, Berlin, 1980).Google Scholar
[6]Grunewald, F. and Lubotzky, A., ‘Linear representations of the automorphism group of a free group’, Preprint, 2006, ArXiv:math0606182. Geom. Funct. Anal. accepted.Google Scholar
[7]Guralnick, M. R., Kantor, W. M., Kassabov, M. and Lubotzky, A., ‘Presentations of finite simple groups: a quantitative approach’, J. Amer. Math. Soc 21(3) (2008), 711744.Google Scholar
[8]Magnus, W., Karrass, A. and Solitar, D., Combinatorial Group Theory: Presentations of Groups in Terms of Generators and Relations (Wiley Interscience, New York, 1966).Google Scholar
[9] V. D. Mazurov and E. I. Khukhro (eds.). The Kourovka Notebook, 16th edn (Russian Academy of Sciences, Siberian Division, Institute of Mathematics, Novosibirsk, 2006) (Unsolved problems in group theory, including archive of solved problems).Google Scholar
[10]Meskin, S., ‘Periodic automorphisms of the two-generator free group’, in: Proc. 2nd Int. Conf. on the Theory of Groups, Australian National University, Canberra, 1973, Lecture Notes in Mathematics, 372 (Springer, Berlin, 1974), pp. 494498.Google Scholar
[11]Neumann, B., ‘Die Automorphismengruppe der freien Gruppen’, Math. Ann. 107 (1933), 367386. (Published 1932.)CrossRefGoogle Scholar
[12]Nielsen, J., Jakob Nielsen: Collected Mathematical Papers, Contemporary Mathematicians, 2 (Birkhäuser, Boston, MA, 1986), Edited and with a preface by Vagn Lundsgaard Hansen.Google Scholar
[13]Nuzhin, Ya. N., ‘On a question of M. Conder’, Mat. Zametki 70(1) (2001), 7987.Google Scholar
[14]Tamburini, M. C. and Wilson, J. S., ‘On the (2,3)-generation of automorphism groups of free groups’, Bull. London Math. Soc. 29(1) (1997), 4348.Google Scholar
[15]Tamburini, M. C. and Zucca, P., ‘On a question of M. Conder’, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Nat. Rend. Lincei (9) Mat. Appl. 11(1) (2000), 57.Google Scholar
[16]Vogtmann, K., ‘The cohomology of automorphism groups of free groups’, in: International Congress of Mathematicians, II, Madrid, 2006 (European Mathematical Society, Zürich, 2006), pp. 11011117.Google Scholar
[17]Vsemirnov, M., ‘The group GL(6,ℤ) is (2,3)-generated’, J. Group Theory 10(4) (2007), 425430.CrossRefGoogle Scholar