Almost equal group multiplications

作者：Woodcock Chris^*

来源：Journal of Pure and Applied Algebra, 2010, 214(8): 1497-1500.

DOI：10.1016/j.jpaa.2009.12.002

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. x) is another group with the same underlying set G and identity element e is an element of G such that I((G,) ()) = I((G,x)) Then we show here that the multiplications and x 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.

• 出版日期2010-8