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A Number Theory Problem Concerning Finite Groups and Rings

Published online by Cambridge University Press:  20 November 2018

Ian G. Connell
Ian G. Connell*
Affiliation:
McGill University
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Let f1(n) denote the number of abelian groups of order n and f2(n) the number of semi-simple rings with n elements. What can be said about the magnitude of fi(n)? We shall prove that one can expect, on the average, about 2.3 groups and 2.5 rings of the kind stated for a given order. First we state without proof the two relevant structure theorems (which are readily available in standard texts).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 7 , Issue 1 , March 1964 , pp. 23 - 34
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Erdös, P. and Szekeres, G., Über die Anzahl der Abelschen Gruppen gegebener Ordnung und über ein verwandtes zahlentheoretisches Problem. Acta Litt. Sci. Szeged, v. 7(1934), pp. 95–102.Google Scholar
2. Hardy, G.H. and Riesz, M., The General Theory of Dirichlet Series. Cambridge Tract No. 18. Google Scholar
3. Wiener, N., The Fourier Integral. Google Scholar