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

Diego Rattaggi

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

Group Theory 2007-05-23 v1

Authors: Diego Rattaggi

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.

Keywords

abelian groups finite group theory finite groups

Cite

@article{arxiv.math/0608292,
  title  = {On direct product subgroups of $\mathrm{SO}_3(\mathbb{R})$},
  author = {Diego Rattaggi},
  journal= {arXiv preprint arXiv:math/0608292},
  year   = {2007}
}

Comments

8 pages

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