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🔗 Not normal (group theory) 📊 Not normal (statistics) 📐 Not normal (technical)
nonnormality

nonnormality

9.9
A subgroup that changes when its elements are moved by other group elements
  • noun
  • /ˌnɒnˈnɔːrməlɪti/
  • Specialized
translation icon : no normalidad
  • The nonnormality of the subgroup means that its elements do not remain unchanged under conjugation by group elements.

Examples

  • The nonnormality of the subgroup prevented the construction of a simple quotient group.

  • Because of its nonnormality, the subgroup did not have the expected symmetry properties.

  • Mathematicians often check for nonnormality when analyzing the structure of groups.

  • The group exhibits nonnormality under certain conditions.

  • Understanding nonnormality is crucial for advanced group theory.

  • In group theory, the concept of nonnormality is essential to understand how certain subgroups behave.

  • Identifying nonnormality in a subgroup can alter the approach mathematicians take when proving theorems.

Synonyms

non-normal
vsnonnormality
  • Specialized
8.8

A subgroup that other group elements can change so it becomes different

names the property of lacking invariance under conjugation in a subgroup

Antonyms

normality
13 3.5

A time when things are usual and happen as expected

Surface Forms

nonnormality singular
nonnormalities plural

Morphology

nonnormality = nonnormal (opaque) = non + normal + ity

Although morphologically built from 'non' + 'normal' + '-ity', the sense refers to the specialized algebraic property of a subgroup being 'normal' in group theory, which an average learner cannot derive from everyday meanings.

Etymology

Nonnormality comes from non- meaning 'not' and normality meaning 'being normal' or 'unchanged'. In group theory a 'normal' subgroup stays the same when you 'move' it by other group members, so nonnormality means the subgroup does not stay the same under those moves.