The principal block of finite groups with dihedral sylow 2-subgroups

POS-groups with some cyclic Sylow subgroups

A finite group G is said to be a POS-group if for each x in G the cardinality of the set {y in G | o(y) = o(x)} is a divisor of the order of G. In this paper we study the structure of POS-groups with some cyclic Sylow subgroups.

Principal 2-Blocks and Sylow 2-Subgroups

Let G be a finite group with Sylow 2-subgroup P 6 G. Navarro–Tiep–Vallejo have conjectured that the principal 2-block of NG(P) contains exactly one irreducible Brauer character if and only if all odd-degree ordinary irreducible characters in the principal 2-block of G are fixed by a certain Galois automorphism σ. By recent work of Navarro–Vallejo it suffices to show this conjecture holds for al...

On rational groups with Sylow 2-subgroups of nilpotency class at most 2

A finite group $G$ is called rational if all its irreducible complex characters are rational valued. In this paper we discuss about rational groups with Sylow 2-subgroups of nilpotency class at most 2 by imposing the solvability and nonsolvability assumption on $G$ and also via nilpotency and nonnilpotency assumption of $G$.

Ranks of the Sylow 2-Subgroups of the Classical Groups

Let S be a 2-group. The rank (normal rank) of S is the maximal dimension of an elementary abelian subgroup (a normal elementary abelian subgroup) of S over Z2. The purpose of this article is to determine the rank and normal rank of S, where S is a Sylow 2-subgroup of the classical groups of odd characteristic.

Finite Groups with p-Sylow Coverings