Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

The nonfinite generation of $ {\rm Aut}(G)$, $ G$ free metabelian of rank $ 3$


Authors: S. Bachmuth and H. Y. Mochizuki
Journal: Trans. Amer. Math. Soc. 270 (1982), 693-700
MSC: Primary 20F28; Secondary 20F16
DOI: https://doi.org/10.1090/S0002-9947-1982-0645339-3
MathSciNet review: 645339
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The group of automorphisms of the free metabelian group of rank $ 3$ is not finitely generated.


References [Enhancements On Off] (What's this?)

  • [1] L. Auslander, The automorphism group of a polycyclic group, Ann. of Math. (2) 89 (1969), 314-322. MR 0271202 (42:6085)
  • [2] S. Bachmuth, Automorphisms of free metabelian groups, Trans. Amer. Math. Soc. 118 (1965), 93-104. MR 0180597 (31:4831)
  • [3] S. Bachmuth and H. Y. Mochizuki, $ IA$-automorphisms of the free metabelian group of rank $ 3$, J. Algebra 55 (1978), 106-115. MR 515763 (80a:20036)
  • [4] S. Bachmuth, E. Formanek and H. Y. Mochizuki, $ IA$-automorphisms of two-generator torsion-free groups, J. Algebra 40 (1976), 19-30. MR 0409668 (53:13420)
  • [5] I. Kaplansky, Fields and rings, Univ. of Chicago Press, Chicago, 1969. MR 0269449 (42:4345)
  • [6] A. Karrass and D. Solitar, The subgroups of a free product of two groups with an amalgamated subgroup, Trans. Amer. Math. Soc. 150 (1970), 227-255. MR 0260879 (41:5499)
  • [7] W. Magnus, On a theorem of Marshall Hall, Ann. of Math. (2) 40 (1939), 764-768. MR 0000262 (1:44b)
  • [8] V. N. Remeslennikov and V. G. Sokolov, Some properties of a Magnus embedding, Algebra i Logika 9 (1970), 566-578; English transl., Algebra and Logic 9 (1970), 342-349. MR 0292920 (45:2001)
  • [9] D. J. Robinson, Finiteness conditions and generalized soluble groups. Part 1, Springer-Verlag, Berlin and New York, 1972. MR 0332989 (48:11314)
  • [10] J. P. Serre, Arbres, amalgames, $ S{L_2}$, Asterisque no. 46, Société Mathématiques de France, 1977.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 20F28, 20F16

Retrieve articles in all journals with MSC: 20F28, 20F16


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1982-0645339-3
Keywords: Free solvable group, linear group, free product with amalgamation
Article copyright: © Copyright 1982 American Mathematical Society

American Mathematical Society