caa a22 4500 606160655 CHVBK 20210128100631.0 cr unu---uuuuu 210128e20150201xx s 000 0 eng 10.1007/s10468-014-9488-5 doi (NATIONALLICENCE)springer-10.1007/s10468-014-9488-5 On the Existence of Johnson Polynomials for Nilpotent Groups [Elektronische Daten] [Mark Lewis, S. Prajapati] Let G be a finite group. We say that G has a Johnson polynomial if there exists a polynomial f(x) ∈ ℤ[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 G is an extra-special 2-group. Generalizing this, we say that G has a generalized Johnson polynomial if f(x) ∈ ℚ[x]. We show that if G has nilpotence class 2, then G has a generalized Johnson polynomial if and only if Z(G) is cyclic. Also, if G is nilpotent and |cd(G)| = 2, then G has a generalized Johnson polynomial if and only if G has nilpotence class 2 and Z(G) is cyclic. Springer Science+Business Media Dordrecht, 2014 p -groups nationallicence Nipotence class nationallicence Total character nationallicence Lewis Mark Department of Mathematical Sciences, Kent State University, 44242, Kent, OH, USA aut Prajapati S. Statistics and Mathematics Unit, Indian Statistical Institute, 8th Mile Mysore Road, 560059, Bangalore, India aut Algebras and Representation Theory Springer Netherlands 18/1(2015-02-01), 205-213 1386-923X 18:1<205 2015 18 10468 https://doi.org/10.1007/s10468-014-9488-5 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10468-014-9488-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Lewis Mark Department of Mathematical Sciences, Kent State University, 44242, Kent, OH, USA aut NATIONALLICENCE 700 1- Prajapati S. Statistics and Mathematics Unit, Indian Statistical Institute, 8th Mile Mysore Road, 560059, Bangalore, India aut NATIONALLICENCE 773 0- Algebras and Representation Theory Springer Netherlands 18/1(2015-02-01), 205-213 1386-923X 18:1<205 2015 18 10468