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On The Number of Groups of Squarefree Order

Published online by Cambridge University Press:  20 November 2018

M. Ram Murty  and
S. Srinivasan
M. Ram Murty
Affiliation:
Department of Mathematics McGill University Montreal, CanadaH3A 2K6
S. Srinivasan
Affiliation:
School of Mathematics Tata Institute of Fundamental Research Bombay 400 005, India
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Abstract

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Let G(n) denote the number of non-isomorphic groups of order n. We prove that for squarefree integers n, there is a constant A such that

where denotes the Euler function. This upper bound is essentially best possible, apart from the constant A.

Keywords

10H26
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 30 , Issue 4 , 01 December 1987 , pp. 412 - 420
Copyright
Copyright © Canadian Mathematical Society 1987

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