Displaying similar documents to “The Abelian defect group conjecture.”

Restricted set addition in Abelian groups: results and conjectures

Vsevolod F. Lev (2005)

Journal de Théorie des Nombres de Bordeaux

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We present a system of interrelated conjectures which can be considered as restricted addition counterparts of classical theorems due to Kneser, Kemperman, and Scherk. Connections with the theorem of Cauchy-Davenport, conjecture of Erdős-Heilbronn, and polynomial method of Alon-Nathanson-Ruzsa are discussed. The paper assumes no expertise from the reader and can serve as an introduction to the subject.

The Ore conjecture

Martin Liebeck, E.A. O’Brien, Aner Shalev, Pham Tiep (2010)

Journal of the European Mathematical Society

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The Ore conjecture, posed in 1951, states that every element of every finite non-abelian simple group is a commutator. Despite considerable effort, it remains open for various infinite families of simple groups. In this paper we develop new strategies, combining character-theoretic methods with other ingredients, and use them to establish the conjecture.

On Brauer’s Height Zero Conjecture

Gabriel Navarro, Britta Späth (2014)

Journal of the European Mathematical Society

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In this paper, the unproven half of Richard Brauer’s Height Zero Conjecture is reduced to a question on simple groups.

The Bloch-Kato conjecture on special values of L -functions. A survey of known results

Guido Kings (2003)

Journal de théorie des nombres de Bordeaux

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This paper contains an overview of the known cases of the Bloch-Kato conjecture. It does not attempt to overview the known cases of the Beilinson conjecture and also excludes the Birch and Swinnerton-Dyer point. The paper starts with a brief review of the formulation of the general conjecture. The final part gives a brief sketch of the proofs in the known cases.