Triangles of Baumslag-Solitar Groups - Mathematics > Group TheoryReport as inadecuate

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Abstract: Our main result is that many triangles of Baumslag-Solitar groups collapse tofinite groups, generalizing a famous example of Hirsch. A triangle ofBaumslag-Solitar groups means a group with three generators, cyclicallyordered, with each generator conjugating some power of the previous one toanother power. There are six parameters, occurring in pairs, and we show thatthe triangle fails to be developable whenever one of the parameters divides itspartner, except for a few special cases. Furthermore, under fairly generalconditions, the group turns out to be finite and solvable of class<4. We obtaina lot of information about finite quotients, even when we cannot determinedevelopability.

Author: Daniel Allcock


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