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Submission: 2010, May 22 (revised 2011, Feb 4, former title: Weak commensurability and forms of Spin_4n)

We give a cohomological criterion for existence of outer automorphisms
of a semisimple algebraic group over an arbitrary field. This
criterion is then applied to the special case of groups of type
D_{2n} over a global field, which completes some of the main
results from the paper "Weakly commensurable arithmetic groups and
isospectral locally symmetric spaces'' (Pub. Math. IHES, 2009) by
Prasad and Rapinchuk and gives a new proof of a result from another
paper by the same authors.

2000 Mathematics Subject Classification: Primary 20G30; Secondary 11E72, 20G15.

Keywords and Phrases: weak commensurability, triality, outer automorphisms

Full text: dvi.gz 25 k, dvi 51 k, ps.gz 856 k, pdf.gz 140 k, pdf 163 k.

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