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- W1998329576 abstract "In a recent paper entitled “A commutative analogue of the group ring” we introduced, for each finite group ( G , ⋅ ) , a commutative graded Z -algebra R ( G , ⋅ ) which has a close connection with the cohomology of ( G , ⋅ ) . The algebra R ( G , ⋅ ) is the quotient of a polynomial algebra by a certain ideal I ( G , ⋅ ) and it remains a fundamental open problem whether or not the group multiplication ⋅ on G can always be recovered uniquely from the ideal I ( G , ⋅ ) . Suppose now that ( G , × ) is another group with the same underlying set G and identity element e ∈ G such that I ( G , ⋅ ) = I ( G , × ) . Then we show here that the multiplications ⋅ and × are at least “almost equal” in a precise sense which renders them indistinguishable in terms of most of the standard group theory constructions. In particular in many cases (for example if ( G , ⋅ ) is Abelian or simple) this implies that the two multiplications are actually equal as was claimed in the previously cited paper." @default.
- W1998329576 created "2016-06-24" @default.
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- W1998329576 date "2010-08-01" @default.
- W1998329576 modified "2023-09-26" @default.
- W1998329576 title "Almost equal group multiplications" @default.
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- W1998329576 doi "https://doi.org/10.1016/j.jpaa.2009.12.002" @default.
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