Hostname: page-component-7b7567c8c-tnzcf Total loading time: 0 Render date: 2026-11-14T21:48:37.230Z Has data issue: false hasContentIssue false
  • English
  • Français

On the capability of groups

Published online by Cambridge University Press:  20 January 2009

Graham Ellis
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 how the third integral homology of a group plays a role in determining whether a given group is isomorphic to an inner automorphism group. Various necessary conditions, and sufficient conditions, for the existence of such an isomorphism are obtained.

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 41 , Issue 3 , October 1998, pp. 487 - 495
Copyright
Copyright © Edinburgh Mathematical Society 1998

References

REFERENCES

1. Baer, R., Groups with preassigned central and central quotient group, Trans. Amer. Math. Soc. 44(1938), 387–412.CrossRefGoogle Scholar
2. Beyl, F. R., Felgner, U. and Schmid, P., On groups occurring as center factor groups, J. Algebra 61 (1979), 161–177.CrossRefGoogle Scholar
3. Beyl, F. R. and Tappe, J., Groups extensions, representations, and the Schur multiplicator (Lecture Notes in Math. 958, Springer, 1982).CrossRefGoogle Scholar
4. Brown, R., Johnson, D. L. and Robertson, E. F., Some computations of nonabelian tensor products of groups, J Algebra 111 (1987), 177–202.CrossRefGoogle Scholar
5. Brown, R. and Loday, J.-L., Van Kampen theorems for diagrams of spaces, Topology 26 (1987), 311–335.CrossRefGoogle Scholar
6. Chiswell, I. M., Collins, D. J. and Huebschmann, J., Aspherical group presentations, Math. Z. 178 (1981), 1–36.CrossRefGoogle Scholar
7. Ellis, G., Nonabelian exterior products of groups and an exact sequence in the homology of groups, Glasgow Math. J. 29 (1987), 13–19.CrossRefGoogle Scholar
8. Ellis, G., On five well-known commutator identities, J. Austral. Math. Soc. Ser. A 54 (1993), 1–19.CrossRefGoogle Scholar
9. Ellis, G., Tensor products and q-crossed modules, J. London Math. Soc. (2) 51 (1995), 243–258.CrossRefGoogle Scholar
10. Hall, M. and Senior, J. K., The groups of order 2n(n ≤ 6) (MacMillan, 1964).Google Scholar
11. Hall, P., The classification of prime-power groups, J. Reine Angew. Math. 182 (1940), 130–141.CrossRefGoogle Scholar
12. Hilton, P. J. and Stammbach, U., A Course in Homological Algebra, (Graduate Texts in Math. 4, Springer, New York, 1971).CrossRefGoogle Scholar