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On the integral cohomology of wreath products

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

Record type: Article

Abstract

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 ].

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Published date: 1997

Identifiers

Local EPrints ID: 29825
URI: http://eprints.soton.ac.uk/id/eprint/29825
ISSN: 0021-8693
PURE UUID: 7d923823-b3c1-4f08-ba18-ec866a13c295
ORCID for Ian J. Leary: ORCID iD orcid.org/0000-0001-8300-4979

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Date deposited: 02 May 2007
Last modified: 17 Jul 2017 15:56

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