Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-28T23:46:27.080Z Has data issue: false hasContentIssue false
  • English
  • Français

Nilpotent groups acting fixed point freely on solvable groups

Published online by Cambridge University Press:  17 April 2009

Beverly J. Bailey
Beverly J. Bailey
Affiliation:
Department of Mathematics, University of Minnesota, Minneapolis, Minnesota, USA; Department of Pure Mathematics, School of General Studies, Australian National University, Canberra, ACT
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.

All groups considered are finite. We enlarge the class of groups for which the conjecture below is known to hold, to include all nilpotent groups A such that every proper subgroup of A is Zp ˜ Zp free for all primes p.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 15 , Issue 3 , December 1976 , pp. 339 - 346
Copyright
Copyright © Australian Mathematical Society 1976

References

[1]Berger, T.R., “Automorphisms of solvable groups”, J. Algebra 27 (1973), 311–340.CrossRefGoogle Scholar
[2]Berger, Thomas R., “Hilpotent fixed point free automorphism groups of solvable groups”, Math. Z. 131 (1973), 305–312.CrossRefGoogle Scholar
[3]Camina, Alan R. and Lockett, F. Peter, “On solvable groups which admit the dihedral group of order eight fixed-point-freely”, Bull. Austral. Math. Soc. 8 (1973), 305–312.CrossRefGoogle Scholar
[4]Gross, Fletcher, “Fixed-point-free operator groups of order 8”, Pacific J. Math. 28 (1969), 357–361.CrossRefGoogle Scholar
[5]Gross, Fletcher, “Elementary abelian operator groups”, Bull. Austral. Math. Soc. 7 (1972), 91–100.CrossRefGoogle Scholar