example of infinite solvable groups

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Let $G$ be a solvable group. It is a well-known Theorem that "the index of every maximal subgroup of $G$ is a power of prime or infinite".
I want to find an example of infinite case.




group-theory




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  • 1




    No. It is finite case!
    – Little girl
    yesterday






  • 2




    Does this one give an example? Semi-direct product of $mathbbQ$ and $mathbbQ^times$: math.stackexchange.com/a/289990/85329
    – CJD
    yesterday











  • I can't believe the comment of the person who voted to close this. Is there a mechanism for reporting clueless close votes?
    – C Monsour
    yesterday










  • @C Monsour I don't think so, but it should be possible to vote against closing.
    – Derek Holt
    yesterday














up vote
3
down vote

favorite












Let $G$ be a solvable group. It is a well-known Theorem that "the index of every maximal subgroup of $G$ is a power of prime or infinite".
I want to find an example of infinite case.




group-theory




share|cite|improve this question

















  • 1




    No. It is finite case!
    – Little girl
    yesterday






  • 2




    Does this one give an example? Semi-direct product of $mathbbQ$ and $mathbbQ^times$: math.stackexchange.com/a/289990/85329
    – CJD
    yesterday











  • I can't believe the comment of the person who voted to close this. Is there a mechanism for reporting clueless close votes?
    – C Monsour
    yesterday










  • @C Monsour I don't think so, but it should be possible to vote against closing.
    – Derek Holt
    yesterday












up vote
3
down vote

favorite









up vote
3
down vote

favorite











Let $G$ be a solvable group. It is a well-known Theorem that "the index of every maximal subgroup of $G$ is a power of prime or infinite".
I want to find an example of infinite case.




group-theory




share|cite|improve this question













Let $G$ be a solvable group. It is a well-known Theorem that "the index of every maximal subgroup of $G$ is a power of prime or infinite".
I want to find an example of infinite case.





group-theory





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited 2 days ago









Ethan Bolker

35.6k54099




35.6k54099









asked 2 days ago









Little girl

1448




1448







  • 1




    No. It is finite case!
    – Little girl
    yesterday






  • 2




    Does this one give an example? Semi-direct product of $mathbbQ$ and $mathbbQ^times$: math.stackexchange.com/a/289990/85329
    – CJD
    yesterday











  • I can't believe the comment of the person who voted to close this. Is there a mechanism for reporting clueless close votes?
    – C Monsour
    yesterday










  • @C Monsour I don't think so, but it should be possible to vote against closing.
    – Derek Holt
    yesterday












  • 1




    No. It is finite case!
    – Little girl
    yesterday






  • 2




    Does this one give an example? Semi-direct product of $mathbbQ$ and $mathbbQ^times$: math.stackexchange.com/a/289990/85329
    – CJD
    yesterday











  • I can't believe the comment of the person who voted to close this. Is there a mechanism for reporting clueless close votes?
    – C Monsour
    yesterday










  • @C Monsour I don't think so, but it should be possible to vote against closing.
    – Derek Holt
    yesterday







1




1




No. It is finite case!
– Little girl
yesterday




No. It is finite case!
– Little girl
yesterday




2




2




Does this one give an example? Semi-direct product of $mathbbQ$ and $mathbbQ^times$: math.stackexchange.com/a/289990/85329
– CJD
yesterday





Does this one give an example? Semi-direct product of $mathbbQ$ and $mathbbQ^times$: math.stackexchange.com/a/289990/85329
– CJD
yesterday













I can't believe the comment of the person who voted to close this. Is there a mechanism for reporting clueless close votes?
– C Monsour
yesterday




I can't believe the comment of the person who voted to close this. Is there a mechanism for reporting clueless close votes?
– C Monsour
yesterday












@C Monsour I don't think so, but it should be possible to vote against closing.
– Derek Holt
yesterday




@C Monsour I don't think so, but it should be possible to vote against closing.
– Derek Holt
yesterday















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