Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-25T08:53:41.347Z Has data issue: false hasContentIssue false
  • English
  • Français

Finite groups which admit a fixed-point-free automorphism group isomorphic to S3

Part of: Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

David Parrott
David Parrott
Affiliation:
University of AdelaideAdelaide, S.A. 5001, Australia
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.

Let G be a finite group of even order coprime to 3. If G admits a fixed-point-free automorphism group isomorphic to the symmetric group on three letters, then we prove that G is soluble.

MSC classification

Secondary: 20D05: Finite simple groups and their classification
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 48 , Issue 3 , June 1990 , pp. 384 - 396
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Dolman, B., Ph. D. Thesis, University of Adelaide, 1984.Google Scholar
[2]Glauberman, G., ‘A characteristic subgroup of a p-stable group’, Canad. J. Math. 20 (1968), 1101–1135.Google Scholar
[3]Glauberman, G., Factorizations in local subgroups of finite groups, (CBMS 33, Amer. Math. Soc., Providence, R.I., 1977).Google Scholar
[4]Gorenstein, D., Finite groups, (Harper and Row, New York, 1968).Google Scholar
[5]Huppert, B. and Blackburn, N., Finite groups II, (Springer-Verlag, Berlin, Heidelberg, New York, 1982).CrossRefGoogle Scholar
[6]Martineau, R. P., ‘Elementary abelian fixed-point-free automorphism groups’, Quart. J. Math. Oxford Ser. (2) 23 (1972), 205–212.CrossRefGoogle Scholar
[7]Rickman, B., ‘Groups which admit a fixed-point-free automorphism of order p2’, J. Algebra 59 (1979), 77–171.Google Scholar
[8]Rowley, P. J., ‘Solubility of finite groups admitting a fixed-point-free abelian automorphism group of square-free exponent rs’, Proc. London Math. Soc. (3) 37 (1978), 385–421.Google Scholar
[9]Shult, E., ‘On groups admitting fixed-point-free abelian operator groups’, Illinois J. Math. 9 (1965), 701–720.Google Scholar
[10]Shult, E., ‘Nilpotence of the commutator subgroup in groups admitting fixed point free operator groups’, Pacific J. Math. 17 (1966), 323–347.Google Scholar