Diameters of Degree Graphs of Nonsolvable Groups, II
نویسندگان
چکیده
Let G be a finite group and let cd(G) be the set of irreducible character degrees of G. The degree graph ∆(G) is the graph whose set of vertices is the set of primes that divide degrees in cd(G), with an edge between p and q if pq divides a for some degree a ∈ cd(G). It is shown using the degree graphs of the finite simple groups that if G is a nonsolvable group, then the diameter of ∆(G) is at most 3.
منابع مشابه
Four-Vertex Degree Graphs of Nonsolvable Groups
For a finite group G, the character degree graph ∆(G) is the graph whose vertices are the primes dividing the degrees of the ordinary irreducible characters of G, with distinct primes p and q joined by an edge if pq divides some character degree of G. We determine all graphs with four vertices that occur as ∆(G) for some nonsolvable group G. Along with previously known results on character degr...
متن کاملFinite imprimitive linear groups of prime degree
In an earlier paper the authors have classified the nonsolvable primitive linear groups of prime degree over C. The present paper deals with the classification of the nonsolvable imprimitive linear groups of prime degree (equivalently, the irreducible monomial groups of prime degree). If G is a monomial group of prime degree r, then there is a projection π of G onto a transitive group H of perm...
متن کاملThe Complexity of the Equivalence Problem for Nonsolvable Groups
The equivalence problem for a group G is the problem of deciding which equations hold in G. It is known that for finite nilpotent groups and certain other solvable groups, the equivalence problem has polynomial-time complexity. We prove that the equivalence problem for a finite nonsolvable group G is co-NP-complete by reducing the k-coloring problem for graphs to the equivalence problem, where ...
متن کامل