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2019•Algebra ColloquiumRequires access

On a Generalized Centralizer Ring of a Finite Group Which Determines the Group

Emma L. Rode

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Abstract

The k-characters are class functions on subsets of Gkcalled the k-classes of G. For a finite group G, the k-class sums form a basis for a subring of ℂGk, which we call the k-S-ring of G, and we think of these rings as generalized centralizer rings. We show that for a finite group G the 3-S-ring determines G. More specifically, the group characters and set products of certain 3-classes of G, which we call “uniform 3-classes”, determine G.

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What this paper is about

The k-characters are class functions on subsets of Gkcalled the k-classes of G. For a finite group G, the k-class sums form a basis for a subring of ℂGk, which we call the k-S-ring of G, and we think of these rings as generalized centralizer rings. We show that for a finite group G the 3-S-ring determines G. More specifically, the group characters and set products of certain 3-classes of G, which we call “uniform 3-classes”, determine G.

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Available abstract

The k-characters are class functions on subsets of Gkcalled the k-classes of G. For a finite group G, the k-class sums form a basis for a subring of ℂGk, which we call the k-S-ring of G, and we think of these rings as generalized centralizer rings. We show that for a finite group G the 3-S-ring determines G. More specifically, the group characters and set products of certain 3-classes of G, which we call “uniform 3-classes”, determine G.

Key concepts: Mathematics, Centralizer and normalizer, Subring, Ring (chemistry), Group ring, Group (periodic table), Finite group, Class (philosophy)

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