Describing the nub in maximal Kac–Moody groups

Abstract Let G be a totally disconnected locally compact (tdlc) group. The contraction group con ( g ) $\mathrm {con}(g)$ con left parenthesis g right parenthesis of an element g ∈ G $g\in G$ g element of upper G is the set of all h ∈ G $h\in G$ h element of upper G such that g n h g − n → 1 G $g^n h g^{-n} \to 1_G$ g Superscript n Baseline h g Superscript negative n Baseline right arrow 1 Subscript upper G as n → ∞ $n \to \infty $ n right arrow infinity . The nub of g can then be characterized as the intersection nub ( g ) $\mathrm {nub}(g)$ nub left parenthesis g right parenthesis of the closures of con ( g ) $\mathrm {con}(g)$ con left parenthesis g right parenthesis and