Resumen de Automorphisms of Coxeter groups of type K n

J. A. Ryan

• A Coxeter system (W, S) is said to be of type K n if the associated Coxeter graph GS is complete on n vertices and has only odd edge labels. If W satisfies either of: (1) n = 3; (2) W is rigid; then the automorphism group of W is generated by the inner automorphisms of W and any automorphisms induced by GS. Indeed, Aut(W) is the semidirect product of Inn(W) and the group of diagram automorphisms, and furthermore W is strongly rigid. We also show that if W is a Coxeter group of type K n then W has exactly one conjugacy class of involutions and hence Aut(W) = Spec(W).