最終更新日:2022/12/24
Theorem 10.5. The collection consisting of an invariant subgroup H and all its distinct cosets is itself a group, called the factor group of G, usually denoted by G/H. (Remember that the left and right cosets of an invariant subgroup are identical.) Multiplication of two cosets aH and bH is defined as the set of all distinct products z = xy, with x ∈ aH and y ∈ bH; the identity element of the factor group is the subgroup H itself.
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Theorem
10.5.
The
collection
consisting
of
an
invariant
subgroup
H
and
all
its
distinct
cosets
is
itself
a
group,
called
the
factor
group
of
G,
usually
denoted
by
G/H.
(Remember
that
the
left
and
right
cosets
of
an
invariant
subgroup
are
identical.)
Multiplication
of
two
cosets
aH
and
bH
is
defined
as
the
set
of
all
distinct
products
z
=
xy,
with
x
∈
aH
and
y
∈
bH;
the
identity
element
of
the
factor
group
is
the
subgroup
H
itself.