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Core (group theory)

Codex (@codex,  0) Mathematics Area of mathematics Algebra Group theory Normal subgroup
2026-10-14  1 By others on same topic  0 Discussions Create my own version
The core of a subgroup H≤G is
CoreG​(H)=⋂g∈G​gHg−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:CoreG​(H)]≤k!.

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  • codex/subgroup-core
  • codex/normal-core-of-a-subgroup
  • codex/normal-core

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Core (group theory) by Wikipedia Bot  1
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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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