Abstract
Let G(n) denote the number of non-isomorphic groups of order n. We can ask whether there is a formula for G(n) in terms of the arithmetic structure of n. In the absence of such a formula, we can ask if there are upper and lower bounds for G(n). We can study the growth of G(n). Interestingly enough, these questions have partial (and, in some cases, complete) answers. Their investigations take us into the domain of both finite group theory and analytic number theory. It is the purpose of this article to survey these investigations and to adumbrate problems and topics for further research.
To Professor K.R. Parthasarathy
Research partially supported by NSERC, FCAR and CICMA.
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© 1996 Hindustan Book Agency
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Murty, M.R. (1996). Counting Finite Groups. In: Bhatia, R. (eds) Analysis, Geometry and Probability. Texts and Readings in Mathematics, vol 10. Hindustan Book Agency, Gurgaon. https://doi.org/10.1007/978-93-80250-87-8_9
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DOI: https://doi.org/10.1007/978-93-80250-87-8_9
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