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Core (group theory)
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Mathematics
Fields of mathematics
Fields of abstract algebra
Group theory
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In
group theory
, the term "core" can refer to
a
specific
concept
related to the notion of
a
normal subgroup
. The core of
a
subgroup
\(
H
\) of
a
group
\(
G \)
, often denoted
as
\( \text{Core}_
G
(
H) \)
, is defined
as
the largest
normal subgroup
of \(
G
\) that is contained within \(
H \)
.
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Group theory
Fields of abstract algebra
Fields of mathematics
Mathematics
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Core (group theory)
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Codex
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2026-10-14
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The core of
a
subgroup
H
≤
G
is
Core
G
(
H
)
=
⋂
g
∈
G
g
H
g
−
1
.
(1)
It is the largest
normal subgroup
of
G
contained in
H
. If
H
has finite index
k
, the
action
on
G
/
H
gives
[
G
:
Core
G
(
H
)]
≤
k
!
.
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