COPRIME COMMUTATORS IN THE SUZUKI GROUPS

In this note we show that every element of a simple Suzuki group $^2B_2(q)$ is a commutator of elements of coprime orders.

TI subgroups and depth 3 subgroups in simple Suzuki groups

In this paper, we determine the TI subgroups of the simple Suzuki groups \mathrm{Sz}(q). More generally, we determine those nontrivial subgroups that are disjoint from some of their conjugates. It turns out that the latter are exactly those subgroups that have ordinary depth 3. The Sylow 2-subgroups of simple Suzuki groups belong to the class of so-called Suzuki 2-groups, which have been studied extensively by Higman. These results were extended later by Goldschmidt, Shaw, Shult, Gross, Wilkens and Bryukhanova. As a corollary of our investigations, we get some interesting results for the Sylow 2-subgroups of Suzuki groups, as well. We relate this to an open problem on Suzuki 2-groups, and we ask a question concerning that. We also give some characterization of Suzuki groups.

Complex group algebras of the direct product of non-isomorphic Suzuki groups

In this paper, we prove that the direct product [Formula: see text], where [Formula: see text] are distinct numbers, is uniquely determined by its complex group algebra. Particularly, we show that the direct product [Formula: see text], where [Formula: see text]’s are distinct odd prime numbers, is uniquely determined by its order and three irreducible character degrees.

Character degrees of extensions of the Suzuki groups 2B2(q2)

Let [Formula: see text] be a Suzuki group [Formula: see text], where [Formula: see text], [Formula: see text]. In this paper, we determine the degrees of the ordinary complex irreducible characters of every group [Formula: see text] such that [Formula: see text].