Erzsébet Horváth

The Depth of Subgroups of Suzuki Groups

We determine the combinatorial depth of certain subgroups of simple Suzuki groups Sz(q), among others, the depth of their maximal subgroups. We apply these results to determine the ordinary depth of these subgroups.

Groups with few conjugacy classes

Let G be a finite group, let p be a prime divisor of the order of G and let k ( G ) be the number of conjugacy classes of G . By disregarding at most finitely many non-solvable p -solvable groups G , we have with equality if and only if if is an integer, and C G ( C p ) = C p . This extends earlier work of Hethelyi, Kulshammer, Malle and Keller.

Real characters in blocks

We consider real versions of Brauer’s k(B) conjecture, Olsson’s conjecture and Eaton’s conjecture. We prove the real version of Eaton’s conjecture for 2-blocks of groups with cyclic defect group and for the principal 2-blocks of groups with trivial real core. We also characterize G-classes, real and rational G-classes of the defect group ofB.