The Number of Finite Groups Whose Element Orders is Given

Details The Number of Finite Groups Whose Element Orders is Given The Number of Finite Groups Whose Element Orders is Given

2005-09-22

arxiv.org/abs/math/0509505v2

Mathematics

Group Theory

17 pages

Scientific paper

The spectrum $\omega(G)$ of a finite group $G$ is the set of element orders of $G$. If $\Omega$ is a non-empty subset of the set of natural numbers, $h(\Omega)$ stands for the number of isomorphism classes of finite groups $G$ with $\omega(G)=\Omega$ and put $h(G)=h(\omega(G))$. We say that $G$ is recognizable (by spectrum $\omega(G)$) if $h(G)=1$. The group $G$ is almost recognizable (resp. nonrecognizable) if $1

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