Finite groups with an irreducible character of large degree

Methods and questions in character degrees of finite groups

“…In this context, probably the most remarkable result is the following, which improves on an earlier result in [11]. Theorem 6.2 (Theorem 2.1 of [21]). Let S be a nonabelian simple group.…”

Character table sudokus

“…The reader might have noticed that the difficulties in our proofs arise from groups with "large" character degrees. Gagola While [9] depends on the classification of the finite simple groups, our proof of Theorem 4 (relying on [13, Proposition 2.1]) is CFSG-free. Due to a construction by Isaacs [11], the bound |G| ≤ e 4 − e 3 is best possible whenever e is a power of a prime.…”

“…Due to a construction by Isaacs [11], the bound |G| ≤ e 4 − e 3 is best possible whenever e is a power of a prime. The authors of [9] have asked to classify those groups. Building on work of Snyder [15] for e = 2, 3, Durfee-Jensen [3] have classified the groups with 2 ≤ e ≤ 6 (there are infinitely many groups for e = 1).…”

Bounds on the largest Kronecker and induced multiplicities of finite groups

“…For general groups, parameter Snyder in [Sny] introduced parameter e(G) defined by b(G) b(G) + e(G) = |G|. Parameter e(G) is closely related to ε(G), and was the motivation for a series of recent papers improving bound on both [HLS,HHN,Isa2,LMT]. 9.2.…”