caa a22 4500 606160620 CHVBK 20210128100630.0 cr unu---uuuuu 210128e20150201xx s 000 0 eng 10.1007/s10468-014-9491-x doi (NATIONALLICENCE)springer-10.1007/s10468-014-9491-x Finite Groups with K 4-Free Prime Graphs [Elektronische Daten] [Zeinab Akhlaghi, Hung Tong-Viet] Let G be a finite group and let cd(G) be the set of all complex irreducible character degrees of G. Let ρ(G) be the set of all primes dividing some degrees in cd(G). The prime graph Δ(G) has vertex set ρ(G) and there is an edge between two distinct vertices p and q if pq divides some degree a∈cd(G). In this paper we show that if Δ(G) is K 4-free, then |ρ(G)|≤7; and moreover, if G is solvable, then |ρ(G)|≤6. These bounds are best possible. Springer Science+Business Media Dordrecht, 2014 Character degrees nationallicence Prime graphs nationallicence Akhlaghi Zeinab School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, 3209, Pietermaritzburg, South Africa aut Tong-Viet Hung School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, 3209, Pietermaritzburg, South Africa aut Algebras and Representation Theory Springer Netherlands 18/1(2015-02-01), 235-256 1386-923X 18:1<235 2015 18 10468 https://doi.org/10.1007/s10468-014-9491-x 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/s10468-014-9491-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Akhlaghi Zeinab School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, 3209, Pietermaritzburg, South Africa aut NATIONALLICENCE 700 1- Tong-Viet Hung School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, 3209, Pietermaritzburg, South Africa aut NATIONALLICENCE 773 0- Algebras and Representation Theory Springer Netherlands 18/1(2015-02-01), 235-256 1386-923X 18:1<235 2015 18 10468