Groupes de tresses et moyennabilité intérieure. (Braid groups and inner amenability) (Q805979)

A group G is called innerly amenable if there is a finitely additive measure \(\mu\) on G-\(\{\) \(1\}\) with values in [0,1] which is invariant under conjugation satisfying \(\mu (G-\{1\})=1\). In particular such a group has infinite conjugation classes \(\neq 1\) (the group is cci). Theorem 1: For a subgroup \(G_ 0\subset G\), \([G:G_ 0]<\infty\), one has (i) If \(G_ 0\) is innerly amenable so is G. (ii) If G is finitely generated, cci, and innerly amenable, so is \(G_ 0\). Theorem 2: For \(n\geq 3\) the commutator subgroups of braid groups and their factor groups by their centres are not innerly G amenable. The second theorem is an application of the first one which rests on a Fubini theorem.