Restricted set addition in Abelian groups:  results and conjectures

Vsevolod F. Lev

Displaying similar documents to “Restricted set addition in Abelian groups: results and conjectures”

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The Ore conjecture

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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 a conjecture of M. E. Watkins on graphical regular representations of finite groups

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On Tate’s refinement for a conjecture of Gross and its generalization

Noboru Aoki (2004)

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We study Tate’s refinement for a conjecture of Gross on the values of abelian $L$ -function at $s = 0$ and formulate its generalization to arbitrary cyclic extensions. We prove that our generalized conjecture is true in the case of number fields. This in particular implies that Tate’s refinement is true for any number field.