On the existence of Johnson polynomials for p-groups
نویسندگان
چکیده
Let G be a finite p-group. We say that G has a Johnson polynomial if there exists a polynomial f(x) ∈ Q[x] and a character χ ∈ Irr(G) so that f(χ) equals the total character for G. In this paper, we show that if G has nilpotence class 2, then G has a Johnson polynomial if and only if Z(G) is cyclic, and we show that if |cd(G)| = 2, then G has a Johnson polynomial if and only if G has nilpotence class 2 and Z(G) is cyclic.
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