MediaWiki API result
This is the HTML representation of the JSON format. HTML is good for debugging, but is unsuitable for application use.
Specify the format parameter to change the output format. To see the non-HTML representation of the JSON format, set format=json.
See the complete documentation, or the API help for more information.
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"comment": "Created page with \"A '''commutator''' is an algebraic expression that measures the failure of two elements to [[commute]]. It occurs throughout [[abstract algebra]], particularly in [[group theory]], [[ring theory]], and [[linear algebra]]. If two elements commute, their commutator is trivial. More generally, the commutator describes the obstruction to exchanging the order of two operations. Commutators are fundamental in the study of noncommutative structures and in the construction of i...\""
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"comment": "Created page with \"A '''quotient group''' is a group obtained by aggregating similar elements of a larger group using an equivalence relation that preserves some of the group structure. == Definitions == Let <math>G</math> be a group and <math>N\\trianglelefteq G</math> a normal subgroup. === Definition via cosets === The quotient group <math>G/N</math> is the set of left cosets <math display=\"block\">G/N:=\\{gN\\mid g\\in G\\}</math>with group operation <math>(gN)(hN):=(gh)N.</math> === Defi...\""
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"timestamp": "2026-04-04T11:27:39Z",
"comment": "Created page with \"|- | '''{{{1|{{{en}}}}}}''' | {{{2|{{{fr}}}}}} | {{{3|{{{de}}}}}} | {{{4|{{{zh-cn|{{{zh-hans|}}}}}}}}} | {{{5|{{{zh-tw|{{{zh-hant|}}}}}}}}} | {{{6|{{{ja}}}}}}\""
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"comment": "Created page with \"The '''first isomorphism theorem''' is a fundamental result in [[abstract algebra]] that describes the relationship between a [[homomorphism]], its [[Kernel (algebra)|kernel]], and its [[Image (mathematics)|image]]. The theorem appears uniformly across algebraic structures such as [[Group (mathematics)|groups]], [[Ring (mathematics)|rings]], and [[Module (mathematics)|modules]], and serves as a prototype for many structural results in algebra. Specifically, given a homeo...\""
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