Outer automorphisms of an infinite simple group - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T11:59:30Z http://mathoverflow.net/feeds/question/112400 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/112400/outer-automorphisms-of-an-infinite-simple-group Outer automorphisms of an infinite simple group Stefan Kohl 2012-11-14T17:57:28Z 2012-11-14T20:40:20Z <p>Let $r(m)$ denote the residue class $r+m\mathbb{Z}$, where $0 \leq r &lt; m$. Given disjoint residue classes $r_1(m_1)$ and $r_2(m_2)$, let the class transposition $\tau_{r_1(m_1),r_2(m_2)}$ be the permutation of $\mathbb{Z}$ which interchanges $r_1+km_1$ and $r_2+km_2$ for every $k \in \mathbb{Z}$ and which fixes everything else.</p> <p>The group ${\rm CT}(\mathbb{Z})$ generated by all class transpositions of $\mathbb{Z}$ is simple (cf. Math. Z. 264 (2010), no. 4, 927-938, <a href="http://dx.doi.org/10.1007/s00209-009-0497-8" rel="nofollow">http://dx.doi.org/10.1007/s00209-009-0497-8</a>).</p> <p>Find the outer automorphism group of ${\rm CT}(\mathbb{Z})$.</p>