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arXiv · 1705.06952

Note on the Number of Finite Groups of a Given Order

A. R. Ashrafi·E. Haghi
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Abstract

Let $n$ be a positive integer and $G(n)$ denote the number of non-isomorphic finite groups of order $n$. It is well-known that $G(n) = 1$ if and only if $(n,ϕ(n)) = 1$, where $ϕ(n)$ and $(a, b)$ denote the Euler's totient function and the greatest common divisor of $a$ and $b$, respectively. The aim of this paper is to first present a new proof for the case of $G(n) = 2$ and then give a solution to the equation of $G(n) = 3$.

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A. R. Ashrafi, E. Haghi. 2017-05-19. Note on the Number of Finite Groups of a Given Order. https://arxiv.org/abs/1705.06952

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