Hostname: page-component-745bb68f8f-grxwn Total loading time: 0 Render date: 2025-01-12T10:56:32.826Z Has data issue: false hasContentIssue false
  • English
  • Français

On groups admitting a noncyclic abelian automorphism group

Published online by Cambridge University Press:  17 April 2009

J.N. Ward
J.N. Ward
Affiliation:
Department of Pure Mathematics, University of Sydney, Sydney, New South Wales.
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 a condition of Kurzwell concerning fixed-points of certain operators on a finite group G is sufficient to ensure that G is soluble. The result generalizes those of Martineau on elementary abelian fixed-point-free operator groups.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 9 , Issue 3 , December 1973 , pp. 363 - 366
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Berger, T.R., “Nilpotent fixed-point-free automorphism groups”, (to appear).Google Scholar
[2]Gorenstein, Daniel, Finite groups (Harper and Row, New York, Evanston, London, 1968).Google Scholar
[3]Kurzweil, Hans, “Auflösbare Gruppen, die eine abelsche Automorphismengruppe gestatten, deren Fixpunktgruppe nilpotent ist”, J. Algebra 10 (1968), 92–101.CrossRefGoogle Scholar
[4]Martineau, R. Patrick, “Solubility of groups admitting a fixed-point-free automorphism group of type (p, p)”, Math. Z. 124 (1972), 67–72.CrossRefGoogle Scholar
[5]Martineau, R. Patrick, “Elementary abelian fixed point free automorphism groups”, Quart. J. Math. Oxford (2) 23 (1972), 205–212.CrossRefGoogle Scholar
[6]Ward, J.N., “Involutory automorphisms of groups of odd order”, J. Austral. Math. Soc. 6 (1966), 480–494.CrossRefGoogle Scholar
[7]Ward, J.N., “Automorphisms of finite groups and their fixed-point groups”, J. Austral. Math. Soc. 9 (1969), 467–477.CrossRefGoogle Scholar
[8]Ward, J.N., “On finite groups admitting automorphisms with nilpotent fixed-point group”, Bull. Austral. Math. Soc. 5 (1971), 281–282.CrossRefGoogle Scholar