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Topologies on finite groups

Published online by Cambridge University Press:  17 April 2009

Sidney A. Morris  and
H.B. Thompson
Sidney A. Morris
Affiliation:
The Flinders University of South Australia. The University of Queensland.
H.B. Thompson
Affiliation:
The Flinders University of South Australia. The University of Queensland.
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Abstract

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It has been shown by D. Stephen that the number N of open sets in a non-discrete topology on a finite set with n elements is not greater than 3 × 2n-2.We show that for admissable topologies on a finite group N ≦ 2n/r, where r is the least order of its non-trivial normal subgroups. This is clearly a sharper bound.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 1 , Issue 3 , December 1969 , pp. 315 - 317
Copyright
Copyright © Australian Mathematical Society 1969

References

[1]Hewitt, Edwin and Ross, Kenneth A., Abstract harmonic analysis, Vol. 1, (Academic Press, New York, 1963).Google Scholar
[2]Husain, Taqdir, Introduction to topological groups, (W.B. Saunders Company, Philadelphia and London, 1966).Google Scholar
[3]Stephen, D., “Topologies on finite sets”, Amer. Math. Monthly 75 (1968), 739–741.Google Scholar