The number of finite index subgroups of Baumslag–Solitar groups
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Gelman obtained a simple formula for the number of finite index subgroups of Baumslag–Solitar groups BS(p, q) = 〈a, t | t −1 a p t = a q 〉, where p and q are coprime integers. We generalize this formula to the case of arbitrary nonzero integers. The proof is obtained by calculating the number of permutations y ∈ S n such that the subgroup of S n generated by x and y, where x is given, is transitive. Bibliography: 4 titles.
KeywordsGreat Common Divisor Canonical Decomposition Great Common Divisor Coprime Integer Independent Cycle
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- 4.S. K. Lando, Lectures on Generating Functions [in Russian], MTsNMO, Moscow (2002); English transl.: Am. Math. Soc., Providence, RI (2003).Google Scholar