On Gupta representations of central extensions. (English) Zbl 0543.20021
See the preview in Zbl 0526.20022.
MSC:
20E22 | Extensions, wreath products, and other compositions of groups |
20F14 | Derived series, central series, and generalizations for groups |
20J05 | Homological methods in group theory |
20E05 | Free nonabelian groups |
20F05 | Generators, relations, and presentations of groups |
Keywords:
lower central series; matrix representation; Gupta representation; torsion element; homology groupCitations:
Zbl 0369.20030; Zbl 0362.20031; Zbl 0519.20029; Zbl 0388.20024; Zbl 0402.20026; Zbl 0526.20022References:
[1] | Baumslag, G., Strebel, R., Thomson, M.W.: On the multiplicator of F/y c R. J. Pure Appl. Algebra16, 121-132 (1980) · Zbl 0426.20025 · doi:10.1016/0022-4049(80)90011-0 |
[2] | Cartan, H., Eilenberg, S.: Homological Algebra. Princeton: Princeton University Press 1956 · Zbl 0075.24305 |
[3] | Gupta, C.K.: The free centre-by-metabelian groups. J. Austral. Math. Soc.16, 294-300 (1973) · Zbl 0275.20061 · doi:10.1017/S144678870001507X |
[4] | Gupta, C.K., Gupta, N.D.: Generalized Magnus embeddins and some applications. Math. Z.160, 75-87 (1978) · doi:10.1007/BF01182332 |
[5] | Hilton, J.P., Stammbach, U.: A course in homological algebra. Graduate Texts in Mathematics4. Berlin-Heidelberg-New York: Springer 1971 · Zbl 0238.18006 |
[6] | Kusmin, J.V.: Free centre-by-metabelian groups, Lie algebras andD-groups. Izv. Akad. Nauk SSSR Ser. Mat.41, 3-33 (1977) [Russian]; English Transl.: Math. USSR-Izv.11, 1-30 (1977) |
[7] | Kusmin, J.V.: On elements of finite order in free groups of some varieties. Mat. Sb.119, 119-131 (1982) [Russian] |
[8] | Kusmin, J.V.: The structure of the free groups of some varieties. Mat. Sb. (to appear) [Russian] |
[9] | Lewin, J., Lewin, T.: On center by abelian by one-relator groups. Comm. Pure Appl. Math.26, 767-774 (1973) · Zbl 0288.20042 · doi:10.1002/cpa.3160260518 |
[10] | ?melkin, A.L.: Wreath products and varieties of groups. Izv. Akad. Nauk SSSR Ser. Mat.29, 149-170 (1965 [Russian] · Zbl 0135.04701 |
[11] | Stöhr, R.: On free central extensions of free nilpotent-by-abelian groups. Preprint, Berlin 1983 |
[12] | Thomson, M.W.: Representations of certain verbal wreath products by matrices. Math. Z.167, 239-257 (1979) · doi:10.1007/BF01174804 |
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