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Let $BS(1,2)= \langle a,b \mid bab^{-1} = a^2 \rangle$.

I would like to know if $Aut(BS(1,2))$ is finitely generated or not. And if yes, what are those generators.

Any help would be deeply appreciated.

Jal
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    http://math.stackexchange.com/questions/825580/the-automorphism-group-of-a-finitely-generated-group : this may be of interest. – paf Aug 10 '16 at 00:34
  • So it is the case that BS(1,2) is not finitely generated but is there an infinite set of generators for $Aut(BS(1,2))$? – Jal Aug 10 '16 at 00:45

1 Answers1

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This automorphism group is finitely generated, according to the reference given in the automorphism group of a finitely generated group

Community
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paf
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    See the middle of the 2nd page of the pdf "Tree actions of automorphism groups" given in my link. It is said : "Also of interest in this context is a further result of Collins[3] giving a finite presentation for Aut(G) in the case where p=1 and |q|>1". – paf Aug 10 '16 at 01:10
  • $\mathrm{Aut}(BS(p,q))$ is not finitely generated if and only if $|p|\neq 1$ and $|q|\neq 1$. – paf Aug 10 '16 at 01:12
  • You are right. I saw that paper by collins, and that answers the question. Thanks. – Jal Aug 10 '16 at 01:16