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2-groups with every automorphism central

Part of: Representation theory of groups Special aspects of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

S. P. Glasby
S. P. Glasby
Affiliation:
Department of Pure Mathematics, The University of Sydney, New South Wales 2006, Australia
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Abstract

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An infinite family of 2-groups is produced. These groups have no direct factors and have a non-abelian automorphism group in which all automorphisms are central.

MSC classification

Secondary: 20F28: Automorphism groups of groups 20D45: Automorphisms
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 41 , Issue 2 , October 1986 , pp. 233 - 236
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Curran, M. J., ‘A non-abelian automorphism group with all automorphisms central’, Bull. Austral. Math. Soc. 26 (1982), 393–397.CrossRefGoogle Scholar
[2]Faudree, R., ‘Groups in which each element commutes with its endomorphic images’, Proc. Amer. Math. Soc. 27 (1971), 236–240.CrossRefGoogle Scholar
[3]Glasby, S. P., 2-groups with every auromorphism central (preprint, The University of Sydney, 1984).Google Scholar
[4]Hall, M. Jr, and Senior, J., The groups of order 2n (n ≦ 6) (Macmillan, New York; Collier-Macmillan, London, 1964).Google Scholar
[5]Jonah, D. and Konvisser, M., ‘Some non-abelian p-groups with abelian automorphism groups’, Arch Math. (Basel) 26 (1975), 131–133.CrossRefGoogle Scholar
[6]Malone, J. J., ‘p-groups with non-abelian automorphism groups and all automorphisms central’, Bull. Austral. Math. Soc. 29 (1984), 35–37.CrossRefGoogle Scholar
[7]Miller, G. A., ‘A non-abelian group whose group of automorphisms is abelian’, Messenger Math. 43 (1913/1914), 124–125.Google Scholar
[8]Saunders, P. R., ‘The central automorphisms of a finite group’, J. London Math. Soc. 44 (1969), 225–228.Google Scholar
[9]Struik, R. R., ‘Some non-abelian 2-groups with abelian automorphism groups’, Arch. Math. (Basel) 39 (1982), 299–302.CrossRefGoogle Scholar