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H2(T, G, ∂) and central extensions for crossed modules

Published online by Cambridge University Press:  20 January 2009

A. R.- Grandjean  and
M. Ladra
A. R.- Grandjean
Affiliation:
Departamento de Álgebra, Universidad de Santiago, Spain, E-mail addresses: granjean@zmat.usc.es ladra@zmat.usc.es
M. Ladra
Affiliation:
Departamento de Álgebra, Universidad de Santiago, Spain, E-mail addresses: granjean@zmat.usc.es ladra@zmat.usc.es
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We prove in this paper that if (T, G, ∂) is a perfect and aspherical (Ker ∂ = 1) crossed module, then it admits a universal central extension, whose kernel is the invariant H2(T, G, ∂), that we introduced in [9].

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 42 , Issue 1 , February 1999 , pp. 169 - 177
Copyright
Copyright © Edinburgh Mathematical Society 1999

References

REFERENCES

1.Brown, R., q-perfect groups and universal q-central extensions, Publ. Math. 34 (1990), 291–297.CrossRefGoogle Scholar
2.Brown, R. and Higgins, P. J., On the connection between the second relative homotopy groups of some related spaces, Proc. London Math. Soc (3) 36 (1978), 193–212.CrossRefGoogle Scholar
3.Brown, R. and Loday, J. L., Van Kampen theorems for diagrams of spaces, Topology 26 (1987), 311–335.CrossRefGoogle Scholar
4.Doncel-Juárez, J. L. and Grandjeán, A. R., q-perfect crossed modules, J. Pure Appl. Algebra 81 (1992), 279–292.CrossRefGoogle Scholar
5.Ellis, G. J., Homology of 2-types, J London Math. Soc. (2) 46 (1992), 1–27.CrossRefGoogle Scholar
6.Hilton, P. J. and Stammbach, U., A course in Homological Algebra (Springer, Berlin, 1971).CrossRefGoogle Scholar
7.Hopf, H., Fundamentalgruppe und zweite Bettische Gruppe, Comment. Math. Helv. 14 (1941/1942), 257–309.CrossRefGoogle Scholar
8.Ladra, M., Módulos Cruzados y Extensiones de Grupos (Ph. D. Thesis, Alxebra 39, Universidad de Santiago de Compostela, 1984).Google Scholar
9.Ladra, M. and Grandjeán, A. R., Crossed modules and homology, J. Pure Appl. Algebra 95 (1994), 41–55.CrossRefGoogle Scholar
10.Norrie, K. J., Crossed Modules and analogues of Group theorems (Ph. D. Thesis, University of London, 1987).Google Scholar
11.Norrie, K. J., Actions and automorphisms of crossed modules, Bull. Soc. Math. France 118 (1990), 129–146.CrossRefGoogle Scholar
12.Stammbach, U., Homology in Group Theory (Lecture Note in Mathematics, 359, Springer, Berlin, 1973).CrossRefGoogle Scholar
13.Whitehead, J. H. C., Combinatorial Homotopy II, Bull. Amer. Math. Soc. 55 (1949), 453–496.CrossRefGoogle Scholar