László Héthelyi

On The Number of Conjugacy Classes of a Finite Solvable Group

We prove that a finite solvable group whose order is divisible by a prime p has at least 2√ p −1 conjugacy classes.

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.

On Oliver’s p-group conjecture: II

Let p be an odd prime and S a finite p-group. B. Oliver’s conjecture arises from an open problem in the theory of p-local finite groups. It is the claim that a certain characteristic subgroup

On a strong form of Oliverʼs p-group conjecture

{\mathfrak{X}(S)}

Groups with few conjugacy classes

of S always contains the Thompson subgroup. In previous work the first two authors and M. Lilienthal recast Oliver’s conjecture as a statement about the representation theory of the factor group

Real characters in blocks

{S/\mathfrak{X}(S)}