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University of Cambridge > Talks.cam > Junior Algebra/Logic/Number Theory seminar > Triality, two geometries and one amalgam non-uniqueness result

## Triality, two geometries and one amalgam non-uniqueness resultAdd to your list(s) Download to your calendar using vCal - Dr. Justin McInroy (Lincoln College, Oxford)
- Friday 04 November 2011, 14:00-15:00
- MR4.
If you have a question about this talk, please contact Joanna Fawcett. A polar space $\Pi$ is a geometry whose elements are the totally isotropic subspaces of a vector space $V$ with respect to either an alternating, Hermitian, or quadratic form. We may form a new geometry $\Gamma$ by removing all elements contained in either a hyperplane $F$ of $\Pi$, or a hyperplane $H$ of the dual $\Pi We will discuss two specific examples arising from the triality in $O+_8(q)$. By considering the stabilisers of a maximal flag, we get an amalgam, or “glueing”, of groups for each example. However, the two examples have “similar” amalgams – this leads to a group recognition result for their automorphism groups, $q^7:G_2(q)$ and $Spin_7(q)$. This talk is part of the Junior Algebra/Logic/Number Theory seminar series. ## This talk is included in these lists:- All CMS events
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