Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-22T05:20:31.096Z Has data issue: false hasContentIssue false
  • English
  • Français

On central automorphisms of finite-by-nilpotent groups

Published online by Cambridge University Press:  20 January 2009

Silvana Franciosi  and
Francesco de Giovanni
Silvana Franciosi
Affiliation:
Istituto di Matematica, Facoltà di Scienze, Università di Salerno, I-84100 Salerno, Italy
Francesco de Giovanni
Affiliation:
Dipartimento di Matematica, Università di Napoli, Via Mezzocannone 8, I-80134 Napoli, Italy
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.

The effect of imposing a certain finiteness condition on the group of central automorphisms of a finite-by-nilpotent group is investigated. In particular it is shown that, if each central automorphism of a finite-by-nilpotent group G has finite order, then the factor group G/Z(G) has finite exponent.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 33 , Issue 2 , June 1990 , pp. 191 - 201
Copyright
Copyright © Edinburgh Mathematical Society 1990

References

REFERENCES

1.Curzio, M., Robinson, D. J. S., Smith, H. and Wiegold, J., Some remarks on central automorphisms of hypercentral groups, Arch. Math. (Basel), to appear.Google Scholar
2.Franciosi, S. and De Giovanni, F., A note on groups with countable automorphism groups, Arch. Math. (Basel) 47 (1986), 12–16.CrossRefGoogle Scholar
3.Franciosi, S., De Giovanni, F. and Robinson, D. J. S., On torsion in groups whose automorphism groups have finite rank, Rocky Mountain J. Math. 17 (1987), 431–445.CrossRefGoogle Scholar
4.Fuchs, L., Infinite Abelian Groups (Academic Press, New York-London, 1970–1973).Google Scholar
5.Hall, M. Jr., The Theory of Groups (MacMillan, New York, 1959).Google Scholar
6.Lennox, J. C. and Robinson, D. J. S., Soluble products of nilpotent groups, Rend. Sem. Mat. Univ. Padova 62 (1980), 261–280.Google Scholar
7.Pettet, M. R., Locally finite groups as automorphism groups, Arch. Math. (Basel) 48 (1987), 1–9.CrossRefGoogle Scholar
8.Robinson, D. J. S., Finiteness Conditions and Generalized Soluble Groups (Springer, Berlin, 1972).CrossRefGoogle Scholar
9.Robinson, D. J. S., The vanishing of certain homology and cohomology groups, J. Pure Appl. Algebra 7 (1976), 145–176.CrossRefGoogle Scholar
10.Robinson, D. J. S., A contribution to the theory of groups with finitely many automorphisms, Proc. London Math. Soc. (3) 35 (1977), 34–54.CrossRefGoogle Scholar
11.Robinson, D. J. S., Homology of group extensions with divisible abelian kernel, J. Pure Appl. Algebra 14 (1979), 145–165.CrossRefGoogle Scholar
12.Robinson, D. J. S., Infinite torsion groups as automorphism groups, Quart. J. Math. Oxford (2) 30 (1979), 351–364.CrossRefGoogle Scholar
13.Robinson, D. J. S., On the homology of hypercentral groups, Arch. Math. (Basel) 32 (1979), 223–226.CrossRefGoogle Scholar
14.Stammbach, U., Homology in Group Theory (Lecture Notes in Mathematics 359, Springer, Berlin, 1973).CrossRefGoogle Scholar
15.Zimmerman, J., Countable torsion FC-groups as automorphism groups, Arch. Math. (Basel) 43 (1984), 108–116.CrossRefGoogle Scholar