Subgroups of finitely presented solvable linear groups

Subgroups of finitely presented solvable linear groups
HTML articles powered by AMS MathViewer

by Michael W. Thomson PDF

Trans. Amer. Math. Soc. 231 (1977), 133-142 Request permission

Let G be a finitely generated solvable linear group. It is shown that there exists a finitely presented solvable linear group H with G embedded in H.

References

M. F. Atiyah and I. G. Macdonald, Introduction to commutative algebra, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1969. MR 0242802
Gilbert Baumslag, Subgroups of finitely presented metabelian groups, J. Austral. Math. Soc. 16 (1973), 98–110. Collection of articles dedicated to the memory of Hanna Neumann, I. MR 0332999
Gilbert Baumslag, A finitely presented solvable group that is not residually finite, Math. Z. 133 (1973), 125–127. MR 327910, DOI 10.1007/BF01237898
Gilbert Baumslag, A finitely presented metabelian group with a free abelian derived group of infinite rank, Proc. Amer. Math. Soc. 35 (1972), 61–62. MR 299662, DOI 10.1090/S0002-9939-1972-0299662-4
Gilbert Baumslag, Finitely presented metabelian groups, Proceedings of the Second International Conference on the Theory of Groups (Australian Nat. Univ., Canberra, 1973) Lecture Notes in Math., Vol. 372, Springer, Berlin, 1974, pp. 65–74. MR 0404462
N. D. Gupta and M. F. Newman, On metabelian groups, J. Austral. Math. Soc. 6 (1966), 362–368. MR 0202835
Gilbert Baumslag, On the subalgebras of certain finitely presented algebras, Bull. Amer. Math. Soc. 82 (1976), no. 1, 95–98. MR 412232, DOI 10.1090/S0002-9904-1976-13974-2

Exact representations for free groups

10

46

C. K. Gupta, A faithful matrix representation for certain centre-by-metabelian groups, J. Austral. Math. Soc. 10 (1969), 451–464. MR 0260893
C. K. Gupta and N. D. Gupta, On the linearity of free nilpotent-by-abelian groups, J. Algebra 24 (1973), 293–302. MR 310061, DOI 10.1016/0021-8693(73)90139-7
P. Hall, Finiteness conditions for soluble groups, Proc. London Math. Soc. (3) 4 (1954), 419–436. MR 72873, DOI 10.1112/plms/s3-4.1.419
Marc Krasner and Léo Kaloujnine, Produit complet des groupes de permutations et problème d’extension de groupes. III, Acta Sci. Math. (Szeged) 14 (1951), 69–82 (French). MR 49892
A. I. Mal′cev, On some classes of infinite soluble groups, Mat. Sbornik N.S. 28(70) (1951), 567–588 (Russian). MR 0043088
V. N. Remeslennikov, An example of a finitely presented solvable group without the maximality condition for normal subgroups, Mat. Zametki 12 (1972), 287–293 (Russian). MR 320154
V. N. Remeslennikov, Finite approximability of metabelian groups, Algebra i Logika 7 (1968), no. 4, 106–113 (Russian). MR 0254137

Bases for identical relations for certain matrix groups

10

46

B. A. F. Wehrfritz, Infinite linear groups. An account of the group-theoretic properties of infinite groups of matrices, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 76, Springer-Verlag, New York-Heidelberg, 1973. MR 0335656