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... we simply try to teach mathematics.
For a finite group G, let Irr(G) denote the set of irreducible characters of G (working over the complex field) and define AD(G) to be This invariant of G first appeared in a 1994 paper of B.E. Johnson under a different guise. Johnson was studying the amenability properties (in the Banach algebraic sense) of Fourier algebras of compact groups, and he showed en route that for a finite group G, the amenability constant of its Fourier algebra coincides with AD(G). From basic character theory, we know that AD(G)≥1, with equality if and only if φ(e)=1 for every φ in Irr(G), i.e. if and only if…
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