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On infinitely presented soluble groups

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Luc Guyot
U Göttingen/MPI
Don, 07/10/2010 - 15:00 - 16:00
MPIM Lecture Hall
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For groups with finitely many generators and relators, one can always obtain a minimal group presentation by deleting redundant relators. I will show that such a process does not apply to infinitely presented groups by exhibiting a finitely generated group with no minimal group presentations. The counterexample I will present is moreover 4-soluble and enjoys very special features within the space of marked groups. I will then investigate where soluble groups are located in the space of marked groups, depending on whether they are finitely presented or not. This is a joint work with Yves de Cornulier.

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