Phrase guide

normal subgroup

noun · 1 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

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1

noun

Meaning 1

A subgroup H of a group G that is invariant under conjugation; that is, for all elements h of H and for all elements g in G, the element ghg−1 is in H.

Definition source: English Wiktionary via Wiktextract

Topics: group-theory, mathematics, sciences

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

The term was coined by Évariste Galois.

Across languages

Translations

11 source translations are retained for this English entry.

  • Finnish: normaali aliryhmä — subgroup that is invariant under conjugation
  • French: sous-groupe distingué — subgroup that is invariant under conjugation
  • German: Normalteiler — subgroup that is invariant under conjugation
  • German: normale Untergruppe — subgroup that is invariant under conjugation
  • Hungarian: normálosztó — subgroup that is invariant under conjugation
  • Icelandic: normleg hlutgrúpa — subgroup that is invariant under conjugation
  • Icelandic: óbreytt hlutgrúpa — subgroup that is invariant under conjugation
  • Italian: sottogruppo normale — subgroup that is invariant under conjugation
  • Italian: sottogruppo invariante — subgroup that is invariant under conjugation
  • Polish: podgrupa normalna — subgroup that is invariant under conjugation
  • Spanish: subgrupo normal — subgroup that is invariant under conjugation