Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-28T15:14:35.717Z Has data issue: false hasContentIssue false
  • English
  • Français

Some applications of group Obstructions

Part of: Foundations Connections with homological algebra and category theory

Published online by Cambridge University Press:  09 April 2009

Yel-Chiang Wu
Yel-Chiang Wu
Affiliation:
Department of Mathematical Sciences, Oakland University, Rochester, Michigan 48063, U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We show that the classical interpretation of H3(G, A) is equivalent to Taylor's solutions of compound extensions of groups. It is also equivalent to the exactness to an eight term sequence. Only halves of the equivalences are fully shown in the paper but the other halves are clear.

MSC classification

Secondary: 20J05: Homological methods in group theory 20A10: Metamathematical considerations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 32 , Issue 2 , April 1982 , pp. 178 - 186
Copyright
Copyright © Australian Mathematical Society 1982

References

[1]Barr, M. and Rinehart, G. S., ‘Cohomology as the derived functors of derivations’, Trans. Amer. Math. Soc. 122 (1966), 416–426.CrossRefGoogle Scholar
[2]Gerstenhaber, M., ‘On the deformation of rings and algebras,’ II, Ann. of Math. 84 (1966), 1–19.CrossRefGoogle Scholar
[3]Huebschmann, J., ‘Extensions de groupes et paires croisées,’ C. R. Acad. Sci. Paris Sér. A 285 (1977), 993–995.Google Scholar
[4]Loday, J.-L., ‘Cohomologie et groupe de Steinberg relatifs,’ J. Algebra 54 (1978), 178–202.CrossRefGoogle Scholar
[5]Lane, S. MacHomology (Springer-Verlag, 1963).CrossRefGoogle Scholar
[6]Ratcliffe, J., ‘Crossed modules,’ Trans. Amer. Math. Soc. 257 (1980), 73–89.CrossRefGoogle Scholar
[7]Taylor, R., ‘Compound group extensions I,’ Trans. Amer. Math. Soc. 75 (1953), 106–135.CrossRefGoogle Scholar
[8]Rinehart, G. S., ‘Satellites and cohomology,’ J. Algebra 12 (1969), 295–329.CrossRefGoogle Scholar
[9]Whitehead, J. H. C., ‘Combinatorial homotopy II,’ Bull. Amer. Math. Soc. 55 (1949), 433–496.Google Scholar
[10]Wu, Y.-C., ‘H3(G, A) and obstructions of group extensions,’ J. Pure Appl. Algebra 12 (1978), 93–100, Erratum, 20 (1981), 103–105.CrossRefGoogle Scholar