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Symmetry group
In
abstract algebra
, the
symmetry group
of an object (
image
,
signal
, etc.) is the
group
of all
transformation
s under which the object is
invariant
with
composition
as the group operation. For a space with a
metric
, it is a
subgroup
of the
isometry group
of the space concerned. If not stated otherwise, this article considers
symmetry
groups in
Euclidean geometry
, but the concept may also be studied in more general contexts as expanded below.
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