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The nonfinite generation of , free metabelian of rank 
Authors:
S. Bachmuth and H. Y. Mochizuki
Journal:
Trans. Amer. Math. Soc. 270 (1982), 693-700
MSC:
Primary 20F28; Secondary 20F16
MathSciNet review:
645339
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Abstract: The group of automorphisms of the free metabelian group of rank is not finitely generated.
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Louis
Auslander, The automorphism group of a polycyclic group, Ann.
of Math. (2) 89 (1969), 314–322. MR 0271202
(42 #6085)
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Bachmuth, Automorphisms of free metabelian
groups, Trans. Amer. Math. Soc. 118 (1965), 93-104. MR 0180597
(31 #4831), http://dx.doi.org/10.1090/S0002-9947-1965-0180597-3
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Seymour
Bachmuth and Horace
Y. Mochizuki, IA-automorphisms of the free metabelian group of rank
3, J. Algebra 55 (1978), no. 1, 106–115.
MR 515763
(80a:20036), http://dx.doi.org/10.1016/0021-8693(78)90194-1
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Seymour
Bachmuth, Edward
Formanek, and Horace
Y. Mochizuki, IA-automorphism of certain two-generator torsion-free
groups, J. Algebra 40 (1976), no. 1,
19–30. MR
0409668 (53 #13420)
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Irving
Kaplansky, Fields and rings, The University of Chicago Press,
Chicago, Ill.-London, 1969. MR 0269449
(42 #4345)
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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), http://dx.doi.org/10.1090/S0002-9947-1970-0260879-9
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Wilhelm
Magnus, On a theorem of Marshall Hall, Ann. of Math. (2)
40 (1939), 764–768. MR 0000262
(1,44b)
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V.
N. Remeslennikov and V.
G. Sokolov, Certain properties of the Magnus imbedding,
Algebra i Logika 9 (1970), 566–578 (Russian). MR 0292920
(45 #2001)
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Derek
J. S. Robinson, Finiteness conditions and generalized soluble
groups. Part 1, Springer-Verlag, New York, 1972. Ergebnisse der
Mathematik und ihrer Grenzgebiete, Band 62. MR 0332989
(48 #11314)
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J. P. Serre, Arbres, amalgames,
, Asterisque no. 46, Société Mathématiques de France, 1977.
- [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,
-automorphisms of the free metabelian group of rank , J. Algebra 55 (1978), 106-115. MR 515763 (80a:20036)
- [4]
- S. Bachmuth, E. Formanek and H. Y. Mochizuki,
-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,
, Asterisque no. 46, Société Mathématiques de France, 1977.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9947-1982-0645339-3
PII:
S 0002-9947(1982)0645339-3
Keywords:
Free solvable group,
linear group,
free product with amalgamation
Article copyright:
© Copyright 1982 American Mathematical Society
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