Pantelis
Eleftheriou,
Department
of
Pure
Mathematics,
University
of
Waterloo
Groups
definable
in
o-minimal
structures
Let
M
be
an
ordered
vector
space
over
an
ordered
division
ring
D.
A
subset
X
of
Mn
is
called
“semilinear”
if
it
is
a
boolean
combination
of
sets
defined
by
linear
equations
and
inequalities
with
coefficients
from
D.
A
”semilinear
group”
is
a
group
whose
domain
and
the
graph
of
its
multiplication
are
semilinear
sets.
We
prove
that
every
semilinear
group
is
semilinearly
isomorphic
to
a
quotient
by
a
lattice,
exemplifying
its
strong
connection
to
a
real
Lie
group.
This
study
belongs
to
the
general
program
of
studying
groups
definable
in
o-minimal
structures.