A faithful matrix representation for certain centre-y-metabelian groups: To Bernhard Hermann Neumann on his 60th birthday

C. K. Gupta

doi:10.1017/S1446788700007710

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It is a well-known result of W. Magnus [3] that there is a faithful matrix representation for metabelian groups i.e the groups satisfying the law ‘x, y; u, v’. The work in this paper arose in an attempt by the author to find a faithful matrix representation for centre-by-metabelian groups i.e. the groups satisfying the law ‘ x, y; u, v].

References

[1]Fox, R. H., ‘Free differential calculus 1: Derivation in the free group ring’, Ann. Math. (2) 57 (1953), 547–560.Google Scholar

[2]Gupta, C. K., ‘Centre-by-metabelian groups’ (Thesis), Austral. Nat. Univ., 1967 Canberra.Google Scholar

[3]Wilhelm, Magnus, ‘On a theorem of Marshall Hall’, Ann. Math. 40 (1939), 764–768.Google Scholar

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Gupta, Narain 1973. Certain commutator subgroups of free groups. Communications on Pure and Applied Mathematics, Vol. 26, Issue. 5-6, p. 699.

Plotkin, B. I. 1973. General theory of groups. Journal of Soviet Mathematics, Vol. 1, Issue. 5, p. 527.

Levin, Frank 1973. On torsion‐free nilpotent varieties. Communications on Pure and Applied Mathematics, Vol. 26, Issue. 5-6, p. 757.

Gupta, C.K and Gupta, N.D 1973. On the linearity of free nilpotent-by-abelian groups. Journal of Algebra, Vol. 24, Issue. 2, p. 293.

Merzlyakov, Yu. I. 1973. Linear groups. Journal of Soviet Mathematics, Vol. 1, Issue. 5, p. 571.

Gupta, Chander Kanta 1973. The free centre-by-metabelian groups. Journal of the Australian Mathematical Society, Vol. 16, Issue. 3, p. 294.

Lewin, Jacques and Lewin, Tekla 1973. On center by abelian by one‐relator groups. Communications on Pure and Applied Mathematics, Vol. 26, Issue. 5-6, p. 767.

Gupta, Narain and Levin, Frank 1974. Generating groups of certain soluble varieties. Journal of the Australian Mathematical Society, Vol. 17, Issue. 2, p. 222.

Fisher, James L. 1974. The poset of skew fields generated by a free algebra. Proceedings of the American Mathematical Society, Vol. 42, Issue. 1, p. 33.

Gupta, Narain and Levin, Frank 1976. Separating laws for free centre -by -metabelian nilpotent groups. Communications in Algebra, Vol. 4, Issue. 3, p. 249.

Brumslag, Gilbert 1976. Multiplicators and metabelian groups. Journal of the Australian Mathematical Society, Vol. 22, Issue. 3, p. 305.

Gupta, N. D. and Wehrfritz, B. A. F. 1976. Some residual properties of certain nilpotent-by-Abelian groups. Archiv der Mathematik, Vol. 27, Issue. 1, p. 449.

Gupta, N.D and Passi, I.B.S 1976. Some properties of fox subgroups of free groups. Journal of Algebra, Vol. 43, Issue. 1, p. 198.

Thomson, Michael W. 1977. Subgroups of finitely presented solvable linear groups. Transactions of the American Mathematical Society, Vol. 231, Issue. 1, p. 133.

Miller, Jay I. 1979. Center-by-metabelian groups of prime exponent. Transactions of the American Mathematical Society, Vol. 249, Issue. 1, p. 217.

Thomson, Michael W. 1979. Representations of certain verbal wreath products by matrices. Mathematische Zeitschrift, Vol. 167, Issue. 3, p. 239.

Miller, Jay I. 1979. Just non-metabelian groups. Mathematische Zeitschrift, Vol. 166, Issue. 1, p. 1.

Stöhr, R. 1980. Freie Produkte torsionsfreier abelscher Gruppen in der Varietät der zentralen Erweiterungen metabelscher Gruppen. Mathematische Nachrichten, Vol. 96, Issue. 1, p. 271.

Kanta Gupta, Chander 1983. Subgroups induced by certain ideals of free group rings. Communications in Algebra, Vol. 11, Issue. 22, p. 2519.

Gupta, C. K. Gupta, N. D. and Levin, F. 1989. On conjugacy p-separability of free centre-by-metabelian groups. Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, Vol. 47, Issue. 2, p. 334.

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