Special and Extra Special Groups

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• Vladimir Vankov, University of Southampton
• Friday 08 February 2019, 15:00-16:00
• CMS, MR14.

If you have a question about this talk, please contact Stacey Law.

Bestvina-Brady presented examples of non-finitely presented groups with finitely presented augmentation ideal. Ian Leary generalised their construction, yielding groups which form uncountably many quasi-isometry classes, are potential candidates to resolve the relation gap problem, and can be used to prove that every countable group embeds into a group with finitely presented augmentation ideal, among other interesting properties. In my work, I apply the theory of special cube complexes, as developed by Daniel Wise, to obtain linear representations of these groups. While playing with the combinatorics of hyperplanes in complexes they act on, the class of extra special p-groups arises as a terminological coincidence when determining finite-index torsion-free subgroups.

This talk is part of the Junior Algebra and Number Theory seminar series.

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