Hostname: page-component-7479d7b7d-k7p5g Total loading time: 0 Render date: 2024-07-14T04:24:36.386Z Has data issue: false hasContentIssue false

Countable periodic CC-groups as automorphism groups

Published online by Cambridge University Press:  20 January 2009

Martyn R. Dixon
Affiliation:
Mathematics DepartmentUniversity of AlabamaBox 870350Tuscaloosa, AL 35487-0350, USA
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.

It is shown that if G is a group and Aut G is a countable periodic CC-group then Aut G is FC.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1992

References

REFERENCES

1.Alcazar, J. and Otal, J., Sylow subgroups of groups with Černikov conjugacy classes, J. Algebra 110 (1987), 507513.CrossRefGoogle Scholar
2.Dixon, M. R. and Evans, M. J., Periodic divisible-by-finite automorphism groups are Finite, J. Algebra 137 (1991), 416424.CrossRefGoogle Scholar
3.Franciosi, S. and De Giovanni, F., A note on groups with countable automorphism groups, Arch. Math. 47 (1986), 1216.CrossRefGoogle Scholar
4.Francosi, S., de Giovanni, F. and Tomkinson, M. J., Groups with Černikov conjugacy classes, J. Austral. Math. Soc. Ser. A 50 (1991), 114.CrossRefGoogle Scholar
5.Menegazzo, F. and Stonehewer, S. E., On the automorphism group of a nilpotent p-group, J. London Math. Soc. (2) 31(1985), 272276.CrossRefGoogle Scholar
6.Otal, J., Peña, J. M. and Tomkinson, M. J., Locally inner automorphisms of CC-groups, J. Algebra 141 (1991), 382398.CrossRefGoogle Scholar
7.Pettet, M. R., Locally finite groups as automorphism groups, Arch. Math. 48 (1987), 19.CrossRefGoogle Scholar
8.Pettet, M. R., Almost-nilpotent periodic groups as automorphism groups, Quart. J. Math. Oxford (2) 41 (1990), 93108.CrossRefGoogle Scholar
9.Robinson, D. J. S., Infinite torsion groups as automorphism groups, Quart. J. Math. Oxford (2) 30 (1979), 351364.CrossRefGoogle Scholar
10.Robinson, D. J. S., Finiteness Conditions and Generalized Soluble Groups, vols. I and II (Springer, Berlin-Heidelberg-New York, 1972).Google Scholar
11.Zimmerman, J., Countable torsion FC-groups as automorphism groups, Arch. Math. 43 (1984), 108116.CrossRefGoogle Scholar