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Not quite inner automorphisms

Published online by Cambridge University Press:  17 April 2009

B. H. Neumann
B. H. Neumann
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, PO Box 4, Canberra, ACT 2600, Australia Division of Mathematics and Statistics, Commonwealth Scientific and Industrial Research Organization, PO Box 1965, Canberra City, ACT 2601, Australia.
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Abstract

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A question asked by G. Kowol is answered by the construction, to an arbitrarily given natural number n, of groups G with automorphisms that agree with inner automorphisms on each set of fewer than n elements of G, but fail to agree with any inner automorphism on at least one set of n elements.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 23 , Issue 3 , June 1981 , pp. 461 - 469
Copyright
Copyright © Australian Mathematical Society 1981

References

[1]Burnside, W., “On the outer isomorphisms of a group”, Proc. London Math. Soc. (2) 11 (1913), 40–42.CrossRefGoogle Scholar
[2]Liebeck, Hans, “Locally inner and almost inner automorphisms”, Arch. Math. (Basel) 15 (1964), 18–27.Google Scholar
[3]Wall, G.E., “Finite groups with class-preserving outer automorphisms”, J. London Math. Soc. 22 (1947), 315–320 (1948).CrossRefGoogle Scholar