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On the residual finiteness of generalised free products of nilpotent groups
Author:
Gilbert Baumslag
Journal:
Trans. Amer. Math. Soc. 106 (1963), 193-209
MSC:
Primary 20.52
MathSciNet review:
0144949
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References |
Similar Articles |
Additional Information
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P.
Hall, The splitting properties of relatively free groups,
Proc. London Math. Soc. (3) 4 (1954), 343–356. MR 0064046
(16,217c)
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A. Hirsch, On infinite soluble groups. III, Proc. London Math.
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W. Gruenberg, Residual properties of infinite soluble groups,
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(19,386a)
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Malcev, On isomorphic matrix representations of infinite
groups, Rec. Math. [Mat. Sbornik] N.S. 8 (50) (1940),
405–422 (Russian, with English summary). MR 0003420
(2,216d)
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Gilbert
Baumslag, A non-hopfian group, Bull. Amer. Math. Soc. 68 (1962), 196–198. MR 0142634
(26 #203), http://dx.doi.org/10.1090/S0002-9904-1962-10743-5
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Levi, Über die Untergruppen der freien Gruppen, Math. Z.
37 (1933), no. 1, 90–97 (German). MR
1545385, http://dx.doi.org/10.1007/BF01474565
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Graham
Higman, A finitely related group with an isomorphic proper factor
group, J. London Math. Soc. 26 (1951), 59–61.
MR
0038347 (12,390b)
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Gilbert
Baumslag, On generalised free products, Math. Z.
78 (1962), 423–438. MR 0140562
(25 #3980)
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B.
H. Neumann, An essay on free products of groups with
amalgamations, Philos. Trans. Roy. Soc. London. Ser. A.
246 (1954), 503–554. MR 0062741
(16,10d)
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H. Neumann, Permutational products of groups, J. Austral.
Math. Soc. 1 (1959/1960), 299–310. MR 0123597
(23 #A922)
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Neumann, Generalized free products with amalgamated subgroups.
II, Amer. J. Math. 71 (1949), 491–540. MR 0030522
(11,8a)
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G. Kurosh, The theory of groups. Vol. I, Chelsea Publishing
Co., New York, N.Y., 1955. Translated and edited by K. A. Hirsch. MR 0071422
(17,124c)
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K. A. Hirsch, On infinite soluble groups. I, Proc. London Math. Soc. 44 (1938), 53-60.
- [14]
P. Hall, A contribution to the theory of groups of prime-power order, Proc. London Math. Soc. 36 (1933), 29-95.
- [15]
Graham
Higman, A remark on finitely generated
nilpotent groups, Proc. Amer. Math. Soc. 6 (1955), 284–285.
MR
0069176 (16,996a), http://dx.doi.org/10.1090/S0002-9939-1955-0069176-5
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Gilbert
Baumslag, Some aspects of groups with unique roots, Acta Math.
104 (1960), 217–303. MR 0122859
(23 #A191)
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P.
Hall, Finiteness conditions for soluble groups, Proc. London
Math. Soc. (3) 4 (1954), 419–436. MR 0072873
(17,344c)
- [18]
Wilhelm
Magnus, Beziehungen zwischen Gruppen und Idealen in einem
speziellen Ring, Math. Ann. 111 (1935), no. 1,
259–280 (German). MR
1512992, http://dx.doi.org/10.1007/BF01472217
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Hanna
Neumann, On varieties of groups and their associated
near-rings, Math. Z. 65 (1956), 36–69. MR 0078374
(17,1183d)
- [1]
- P. Hall, The splitting properties of relatively free groups, Proc. London Math. Soc. 4 (1954), 343-356. MR 0064046 (16:217c)
- [2]
- K. A. Hirsch, On infinite soluble groups. III, Proc. London Math. Soc. 49 (1946), 184-194. MR 0017281 (8:132a)
- [3]
- K. W. Gruenberg, Residual properties of infinite soluble groups, Proc. London Math. Soc. 7 (1957), 29-62. MR 0087652 (19:386a)
- [4]
- A. I. Mal'cev, On isomorphic matrix representations of infinite groups, Mat. Sb. (N. S.) 8 (50) (1940), 405-421. MR 0003420 (2:216d)
- [5]
- G. Baumslag, A non-hopfian group, Bull. Amer. Math. Soc. 68 (1962), 196-198. MR 0142634 (26:203)
- [6]
- F. Levi, Über die Untergruppen der freien Gruppen. II, Math. Z. 37 (1933), 90-97. MR 1545385
- [7]
- G. Higman, A finitely related group with an isomorphic proper factor group, J. London Math. Soc. 26 (1951), 59-61. MR 0038347 (12:390b)
- [8]
- G. Baumslag, On generalised free products, Math. Z. 78 (1962), 423-438. MR 0140562 (25:3980)
- [9]
- B. H. Neumann, An essay on free products of groups with amalgamations, Philos. Trans. Roy. Soc. London Ser. A 246 (1954), 503-554. MR 0062741 (16:10d)
- [10]
- -, Permutational products of groups, J. Austral. Math. Soc. 1 (1960), 299-310. MR 0123597 (23:A922)
- [11]
- H. Neumann, Generalised free products with amalgamated subgroups. II, Amer. J. Math. 71 (1949), 491-540. MR 0030522 (11:8a)
- [12]
- A. G. Kurosh, The theory of groups, Vols. I and II, Chelsea, New York, 1955. English transl, by K. A. Hirsch. MR 0071422 (17:124c)
- [13]
- K. A. Hirsch, On infinite soluble groups. I, Proc. London Math. Soc. 44 (1938), 53-60.
- [14]
- P. Hall, A contribution to the theory of groups of prime-power order, Proc. London Math. Soc. 36 (1933), 29-95.
- [15]
- G. Higman, A remark on finitely generated nilpotent groups, Proc. Amer. Math. Soc. 6 (1955), 284-285. MR 0069176 (16:996a)
- [16]
- G. Baumslag, Some aspects of groups with unique roots, Acta Math. 104 (1960), 217-303. MR 0122859 (23:A191)
- [17]
- P. Hall, Finiteness conditions for soluble groups, Proc. London Math. Soc. 4 (1954), 419-436. MR 0072873 (17:344c)
- [18]
- W. Magnus, Beziehungen zwischen Gruppen und Idealen in einem speziellen Ring, Math. Ann. 111 (1935), 259-280. MR 1512992
- [19]
- H. Neumann, On varieties of groups and their associated near-rings, Math. Z. 65 (1956), 36-69. MR 0078374 (17:1183d)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9947-1963-0144949-8
PII:
S 0002-9947(1963)0144949-8
Article copyright:
© Copyright 1963 American Mathematical Society
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