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CATEGORIES:Algebra Seminar
SUMMARY:A class of groups universal for free R-tree action
s - Thomas Müller\, Queen Mary\, University of Lon
don
DTSTART:20100114T160000Z
DTEND:20100114T170000Z
UID:TALK260AT
URL:/talk/index/260
DESCRIPTION:I report on a new construction in group theory giv
ing rise to a kind of continuous analogue of free
groups. More explicitly\, given any (discrete) gro
up _G_\, we construct a group _RF_(_G_) equipped w
ith a natural (real-valued) Lyndon length function
\, and thus with a canonical action on an associat
ed _*R*_-tree X_{_G_}\, which turns\nout t
o be transitive. Analysis of these groups _RF_(_G_
) is difficult. However\, conjugacy of hyperbolic
elements is understood\, as are the centralizers a
nd normalizers of hyperbolic elements\; moreover\,
we show that _RF_-groups and their associated _*R
*_-trees are universal (with respect to inclusion)
for free _*R*_-tree actions. Furthermore\, we pro
ve\nthat\n\n|_RF_(_G_)| = |_G_|^{2^ℵ0^}\,\n\nand that non-trivial normal subgroup
s of _RF_(_G_) contain a free subgroup of rank |_R
F_(_G_)|\, as well as a number of further structur
al properties of _RF_(_G_) and its quotient\nby th
e span of the elliptic elements.\n
LOCATION:Watson Building\, Lecture Room A
CONTACT:Simon Goodwin
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