On the integral cohomology of wreath products

Leary, Ian J. (1997) On the integral cohomology of wreath products. Journal of Algebra, 198, (1), 184-239. (doi:10.1006/jabr.1997.7151).


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Original Publication URL: http://dx.doi.org/10.1006/jabr.1997.7151


We use the techniques pioneered by Nakaoka to study the integral cohomology of wreath products. The situation is considerably more complicated than for field coefficients. We describe the cohomology of H wr C for C cyclic of prime order and any H whose cohomology is finitely generated in each degree. We discuss various related results and conjectures concerning the exponent of integral cohomology of finite groups. These include a conjecture of A. Adem (recently solved by J. Pakianathan), conjectures of J. Carlson (one solved in this work), and some of our own. One example given is a 2-group whose index-four subgroups have non-trivial intersection, but whose integral cohomology has exponent four, answering a question posed in [ 8 ].

Item Type: Article
ISSNs: 0021-8693 (print)
Related URLs:
Subjects: Q Science > QA Mathematics
Divisions: University Structure - Pre August 2011 > School of Mathematics > Pure Mathematics
ePrint ID: 29825
Date Deposited: 02 May 2007
Last Modified: 06 Aug 2015 02:30
URI: http://eprints.soton.ac.uk/id/eprint/29825

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