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SUMMARY:George Willis (University of Newcastle)
DTSTART:20210830T080000Z
DTEND:20210830T090000Z
DTSTAMP:20260423T052830Z
UID:SiN/29
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SiN/29/">Con
 structing groups with flat-rank greater than 1</a>\nby George Willis (Univ
 ersity of Newcastle) as part of Symmetry in Newcastle\n\n\nAbstract\nThe c
 ontraction subgroup for $x$ in the locally compact group\, $G$\, $\\mathop
 {con}(x) = \\left\\{ g\\in G \\mid x^ngx^{-n} \\to 1\\text{ as }n\\to\\inf
 ty \\right\\}$\, and the Levi subgroup is $\\mathop{lev}(x) = \\left\\{ g\
 \in G \\mid \\{x^ngx^{-n}\\}_{n\\in\\mathbb{Z}} \\text{ has compact closur
 e}\\right\\}$. The following will be shown.\n\nLet $G$ be a totally discon
 nected\, locally compact group and $x\\in G$. Let $y\\in{\\sf lev}(x)$. Th
 en there are $x'\\in G$ and a compact subgroup\, $K\\leq G$ such that: $K$
  is normalised by $x'$ and $y$\, $\\mathop{con}(x') = \\mathop{con}(x)$ an
 d $\\mathop{lev}(x') = \\mathop{lev}(x)$\, and the group $\\langle x'\,y\,
 K\\rangle$ is abelian modulo $K$\, and hence flat.\n\n\nIf no compact open
  subgroup of $G$ normalised by $x$ and no compact open subgroup of $\\math
 op{lev}(x)$ normalised by $y$\, then the flat-rank of $\\langle x'\,y\,K\\
 rangle$ is equal to $2$.\n
LOCATION:https://researchseminars.org/talk/SiN/29/
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