Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 133 / 2 / a / i / Solution

WriteIts Bass-Serre tree has verticesand edges $G/C$, where $C=⟨u^2⟩=⟨v^3⟩$; the edge $gC$ joins $g⟨u⟩$ to $g⟨v⟩$. Sincethis is the infinite $(2,3)$-biregular tree: every $u$-type vertex has degree two and every $v$-type vertex has degree three.