On direct product subgroups of $\mathrm{SO}_3(\mathbb{R})$

Diego Rattaggi

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On direct product subgroups of $\mathrm{SO}_3(\mathbb{R})$

Diego Rattaggi

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Abstract

Let $G_1 \times G_2$ be a subgroup of $\mathrm{SO}_3(\mathbb{R})$ such that the two factors $G_1$ and $G_2$ are non-trivial groups. We show that if $G_1 \times G_2$ is not abelian, then one factor is the (abelian) group of order 2, and the other factor is non-abelian and contains an element of order 2. There exist finite and infinite such non-abelian subgroups.

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BibTeX RIS

Diego Rattaggi. 2006-08-11. On direct product subgroups of $\mathrm{SO}_3(\mathbb{R})$. https://arxiv.org/abs/math/0608292

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