See normal subgroup in All languages combined, or Wiktionary
Download JSON data for normal subgroup meaning in English (3.4kB)
{
"etymology_text": "The term was coined by Évariste Galois.",
"forms": [
{
"form": "normal subgroups",
"tags": [
"plural"
]
}
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"expansion": "normal subgroup (plural normal subgroups)",
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"lang_code": "en",
"pos": "noun",
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"glosses": [
"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."
],
"id": "en-normal_subgroup-en-noun-p0OHTyS2",
"links": [
[
"group theory",
"group theory"
],
[
"invariant",
"invariant"
],
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],
"raw_glosses": [
"(group theory) 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."
],
"topics": [
"group-theory",
"mathematics",
"sciences"
],
"translations": [
{
"code": "fi",
"lang": "Finnish",
"sense": "subgroup that is invariant under conjugation",
"word": "normaali aliryhmä"
},
{
"code": "fr",
"lang": "French",
"sense": "subgroup that is invariant under conjugation",
"tags": [
"masculine"
],
"word": "sous-groupe distingué"
},
{
"code": "de",
"lang": "German",
"sense": "subgroup that is invariant under conjugation",
"tags": [
"masculine"
],
"word": "Normalteiler"
},
{
"code": "de",
"lang": "German",
"sense": "subgroup that is invariant under conjugation",
"tags": [
"feminine"
],
"word": "normale Untergruppe"
},
{
"code": "is",
"lang": "Icelandic",
"sense": "subgroup that is invariant under conjugation",
"tags": [
"feminine"
],
"word": "normleg hlutgrúpa"
},
{
"code": "is",
"lang": "Icelandic",
"sense": "subgroup that is invariant under conjugation",
"tags": [
"feminine"
],
"word": "óbreytt hlutgrúpa"
},
{
"code": "it",
"lang": "Italian",
"sense": "subgroup that is invariant under conjugation",
"tags": [
"masculine"
],
"word": "sottogruppo normale"
},
{
"code": "it",
"lang": "Italian",
"sense": "subgroup that is invariant under conjugation",
"tags": [
"masculine"
],
"word": "sottogruppo invariante"
},
{
"code": "pl",
"lang": "Polish",
"sense": "subgroup that is invariant under conjugation",
"tags": [
"feminine"
],
"word": "podgrupa normalna"
},
{
"code": "es",
"lang": "Spanish",
"sense": "subgroup that is invariant under conjugation",
"tags": [
"masculine"
],
"word": "subgrupo normal"
}
],
"wikipedia": [
"normal subgroup",
"Évariste Galois"
]
}
],
"word": "normal subgroup"
}
{
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"glosses": [
"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."
],
"links": [
[
"group theory",
"group theory"
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[
"invariant",
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],
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"conjugation"
]
],
"raw_glosses": [
"(group theory) 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."
],
"topics": [
"group-theory",
"mathematics",
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"wikipedia": [
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"translations": [
{
"code": "fi",
"lang": "Finnish",
"sense": "subgroup that is invariant under conjugation",
"word": "normaali aliryhmä"
},
{
"code": "fr",
"lang": "French",
"sense": "subgroup that is invariant under conjugation",
"tags": [
"masculine"
],
"word": "sous-groupe distingué"
},
{
"code": "de",
"lang": "German",
"sense": "subgroup that is invariant under conjugation",
"tags": [
"masculine"
],
"word": "Normalteiler"
},
{
"code": "de",
"lang": "German",
"sense": "subgroup that is invariant under conjugation",
"tags": [
"feminine"
],
"word": "normale Untergruppe"
},
{
"code": "is",
"lang": "Icelandic",
"sense": "subgroup that is invariant under conjugation",
"tags": [
"feminine"
],
"word": "normleg hlutgrúpa"
},
{
"code": "is",
"lang": "Icelandic",
"sense": "subgroup that is invariant under conjugation",
"tags": [
"feminine"
],
"word": "óbreytt hlutgrúpa"
},
{
"code": "it",
"lang": "Italian",
"sense": "subgroup that is invariant under conjugation",
"tags": [
"masculine"
],
"word": "sottogruppo normale"
},
{
"code": "it",
"lang": "Italian",
"sense": "subgroup that is invariant under conjugation",
"tags": [
"masculine"
],
"word": "sottogruppo invariante"
},
{
"code": "pl",
"lang": "Polish",
"sense": "subgroup that is invariant under conjugation",
"tags": [
"feminine"
],
"word": "podgrupa normalna"
},
{
"code": "es",
"lang": "Spanish",
"sense": "subgroup that is invariant under conjugation",
"tags": [
"masculine"
],
"word": "subgrupo normal"
}
],
"word": "normal subgroup"
}
This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-05-05 from the enwiktionary dump dated 2024-05-02 using wiktextract (f4fd8c9 and c9440ce). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
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