Normalizer & normal subgroup related

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SUMMARY

The discussion clarifies that a subgroup H is a normal subgroup of its normalizer in a group G. This conclusion is reached by closely examining the definition of normalizers. The participant acknowledges their initial misunderstanding and emphasizes the clarity of the relationship between normal subgroups and their normalizers.

PREREQUISITES
  • Understanding of group theory concepts, specifically normal subgroups.
  • Familiarity with the definition and properties of normalizers in group theory.
  • Basic knowledge of set notation and subgroup notation.
  • Experience with mathematical proofs and logical reasoning.
NEXT STEPS
  • Study the properties of normal subgroups in more depth.
  • Learn about the implications of normalizers in group actions.
  • Explore examples of normal subgroups and their normalizers in finite groups.
  • Investigate the role of normalizers in the context of group homomorphisms.
USEFUL FOR

Mathematicians, students of abstract algebra, and anyone studying group theory who seeks to understand the relationship between normal subgroups and their normalizers.

iibewegung
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[SOLVED] Normalizer & normal subgroup related

Let [tex]H \subset G[/tex].
Why is [tex]H[/tex] a normal subgroup of its own normalizer in [tex]G[/tex]?
 
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Sorry for wasting space... I figured it out.
(wasn't reading the definition of normalizers carefully)

It was one of those things that one could attach "Clearly," at the front of the statement.

Unfortunately, this leads to another question...
How do I delete this thread?
 
Last edited:

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