examples of outer automorphism group

It is easy to understand that Out=Aut=/2, since is abelianMathworldPlanetmath and there are no inner-automorphisms, save the trivial one.

Also, it is known that OutSL(2,)=/2

Another example is that, at least for orientable surfaces, the extended mapping class groupPlanetmathPlanetmath (or the zeroth homeotopy group) of a surface F is related to its fundamental groupMathworldPlanetmathPlanetmath via *(F)=Out(π1(F)).

1. L. K. Hua, I Reiner AutomorphismsPlanetmathPlanetmathPlanetmath of unimodular groupMathworldPlanetmathPlanetmath, Trans Amer. Math. Soc. 71 (1951), 331-348.

2. H. Zieschang, E. Vogt, H. D. Coldewey, Surfaces and planar discontinuous groups, L.N.M. 875 (1981) Springer-Verlag.

Title examples of outer automorphism group
Canonical name ExamplesOfOuterAutomorphismGroup
Date of creation 2013-03-22 16:30:25
Last modified on 2013-03-22 16:30:25
Owner juanman (12619)
Last modified by juanman (12619)
Numerical id 8
Author juanman (12619)
Entry type Example
Classification msc 20F28