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A non-abelian automorphism group with all automorphisms central

Published online by Cambridge University Press:  17 April 2009

M.J. Curran
M.J. Curran
Affiliation:
Mathematical Institute, University of Oxford, 24–29 St Giles, Oxford 0X1 3LB, England.
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Abstract

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This paper provides an example of a non-abelian 2-group with a non-abelian automorphism group in which every automorphism is central.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 26 , Issue 3 , December 1982 , pp. 393 - 397
Copyright
Copyright © Australian Mathematical Society 1982

References

[1]Earnley, Bruce E., “On finite groups whose group of automorphisms is abelian” (PhD thesis, Wayne State University, Detroit, Michigan, 1975). See also: Dissertation Abstracts, 36 (1976), 2269B.Google Scholar
[2]Gorenstein, Daniel, Finite groups (Harper and Row, New York, Evanston and London, 1968).Google Scholar
[3]Hall, Marshall Jr, and Senior, James K., The groups of order 2n (n ≤ 6) (Macmillan, New York; Collier-Macmillan, London, 1964).Google Scholar
[4]Heineken, Hermann and Liebeck, Hans, “The occurrence of finite groups in the automorphism group of nilpotent groups of class 2”, Arch. Math. (Basel) 25 (1974), 8–16.CrossRefGoogle Scholar
[5]Hughes, Anthony, “Automorphisms of nilpotent groups and supersolvable orders”, The Santa Cruz Conference on Finite Groups, 205–207 (Proceedings of Symposia in Pure Mathematics, 37. American Mathematical Society, Providence, Rhode Island, 1980).CrossRefGoogle Scholar
[6]Jonah, D. and Konvisser, M., “Some non-abelian p-groups with abelian automorphism groups”, Arch. Math. (Basel) 26 (1975), 131–133.CrossRefGoogle Scholar
[7]Miller, G.A., “A non-abelian group whose group of isomorphisms is abelian”, Messenger Math. 43 (1913/1914), 124–125.Google Scholar
[8]Struik, Ruth Rebekka, “Some non-abelian 2-groups with abelian automorphism groups”, Arch. Math. (Basel) (to appear).Google Scholar