See normal subgroup on Wiktionary
{
"etymology_text": "The term was coined by Évariste Galois.",
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{
"form": "normal subgroups",
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"expansion": "normal subgroup (plural normal subgroups)",
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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",
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"(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."
],
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"group-theory",
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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"
}
],
"wikipedia": [
"normal subgroup",
"Évariste Galois"
]
}
],
"word": "normal subgroup"
}
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"glosses": [
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],
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"(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."
],
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"group-theory",
"mathematics",
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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"
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"word": "sous-groupe distingué"
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{
"code": "de",
"lang": "German",
"sense": "subgroup that is invariant under conjugation",
"tags": [
"masculine"
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"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"
}
Download raw JSONL data for normal subgroup meaning in All languages combined (2.8kB)
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-11-06 from the enwiktionary dump dated 2024-10-02 using wiktextract (fbeafe8 and 7f03c9b). 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.
If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.