Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Let $V$ be a virtually cyclic group. Then is $Aut(V)$ also a virtually cyclic group?

This is true when $V$ is a finite group (zero-ended) and when $V = C_\infty, D_\infty$ (both two-ended).

share|improve this question

1 Answer 1

up vote 8 down vote accepted

In Finitely generated groups with virtually free automorphism groups, by M.R. Pettet, it is proved in theorem 3.4 that the automorphism group $Aut(G)$ of a finitely generated group is virtually cyclic if and only if both $Z(G)$ and $G/Z(G)$ are virtually cyclic.

share|improve this answer
    
Excellent, thanks! –  Qayum Khan Aug 7 '11 at 8:51

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.