Connectedness of degree graphs of nonsolvable groups

Character degrees of extensions of PSL2(q) and SL2(q)

“…Several of these studies required increasingly detailed information about the character degrees of groups H with L 2 .q/ 6 H 6 Aut.L 2 .q// (see [5][6][7][8]). Of course, the character table of L 2 .q/ is well known, as is the automorphism group, and so the character degrees of H are known in principle.…”

Some linear actions of finite groups with q′-orbits

“…Condition N q has been recently considered by Zhang [12], by Lewis and White [8], and by Palfy [10], in connection with questions about the set of character degrees of finite groups. The description of the pairs ðG; MÞ satisfying N q when G is soluble (Corollary 10, see also [10]) is a fairly easy application of the aforementioned results of Manz and Wolf.…”

“…We leave this case for further investigation. As in [8] and [12], where the property N q was introduced, motivation comes from its relevance to questions regarding conjugacy class sizes and degrees of irreducible characters. Our Main Theorem is used as a central tool in [3], in order to describe finite groups G in which no conjugacy class size is divisible by the product of two fixed prime divisors of the order of G.…”

Strongly connective degree sets I: nonabelian solvable quotients

“…To show correspondences between the group theoretic structure of G and the arithmetic structure of cd(G), the graph (G) has proven quite useful, as demonstrated in [3] and [4] where groups with disconnected graphs were classified.…”