Almost equal group multiplications

Woodcock, Chris F. (2010) Almost equal group multiplications. Journal of Pure and Applied Algebra, 214 (8). pp. 1497-1500. ISSN 0022-4049. (doi:10.1016/j.jpaa.2009.12.002) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:23811)

 The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. (Contact us about this Publication) Official URLhttp://dx.doi.org/10.1016/j.jpaa.2009.12.002

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,R- ) which has a close connection with the cohomology of (G, ). The algebra R-(G,R-) 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,I- ()).

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- ()) = I-(G,I-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.) is Abelian or simple) this implies that the two multiplications are actually equal as was claimed in the previously cited paper

Item Type: Article 10.1016/j.jpaa.2009.12.002 Q Science > QA Mathematics (inc Computing science) > QA150 Algebra Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Pure Mathematics Christopher Woodcock 07 Sep 2010 08:52 UTC 06 Feb 2020 04:05 UTC https://kar.kent.ac.uk/id/eprint/23811 (The current URI for this page, for reference purposes) https://orcid.org/0000-0003-4713-0040