Abstract
We study the injective endomorphisms φ of the Baumslag–Solitar group G(n,m)= 〈a,t | t-1 ant=am〉 for n, m ∈ ℤ∖{0} such that n, m ≠ ± 1, and show that φ (a) ∈ ∪ i ∈ ℤ∖{0} (ai)G. The proof is based on the Bass–Serre theory of graphs of groups.
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