2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115383Let $G_1 \times G_2$ 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.8 pagesGroup Theorytext