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Glite Dictionary
📊 Not standard 🔢 Not commuting 🧩 Not invariant
non-normal

non-normal

8.8
A subgroup that other group elements can change so it becomes different
  • adjective
  • /nɒnˈnɔːrməl/
  • Specialized
translation icon : no normal
  • The mathematician provided an example of a non-normal subgroup to illustrate the concept.

Examples

  • Identifying whether a subgroup is non-normal can affect the structure of the group.

  • A non-normal subgroup can complicate calculations in group theory.

  • In this group, the non-normal subgroups require special attention during classification.

  • Is this matrix non-normal?

  • In this group, the non-normal subgroups require special attention during classification.

  • The mathematician provided an example of a non-normal subgroup to illustrate the concept.

  • Identifying whether a subgroup is non-normal can affect the structure of the group.

Surface Forms

non-normal positive

Morphology

non-normal = normal (semi-transparent) = non + normal

Formally non- + normal is transparent, but the group-theoretic meaning of 'normal' (invariant under conjugation) is technical and not obvious to general learners.

Etymology

Non-normal is formed from non- ('not') and normal, originally meaning a rule or builder's 'square', so 'normal' means 'following the rule'. In group theory a non-normal subgroup is one that does not stay the same when moved around by the whole group, and that is why it changes the group's structure.