On the embedding of a finite group as Frattini subgroup.
On the Genus of a Nilpotent Group with Finite Commutator Subgroup.
On the group of automorphisms of finite wreath products
On the Isomorphism of Group Algebras.
On the isomorphism problem for modular group algebras of elementary abelian-by-cyclic p-groups
Let G be a finite p-group and let F be the field of p elements. It is shown that if G is elementary abelian-by-cyclic then the isomorphism type of G is determined by FG.
On the Loewy-series of the modular group algebra of a finite p-group.
On the number of solutions of equation in a finite group
Theorem A yields the condition under which the number of solutions of equation in a finite -group is divisible by (here is a fixed positive integer). Theorem B which is due to Avinoam Mann generalizes the counting part of the Sylow Theorem. We show in Theorems C and D that congruences for the number of cyclic subgroups of order which are true for abelian groups hold for more general finite groups (for example for groups with abelian Sylow -subgroups).
On the -length of the product of two Shmidt groups.
On the rarity of quasinormal subgroups
On the regular Sylow -subgroups of Chevalley groups over .
On the Splitting of Extensions by a Group of Prime Order.
On the structure of finite loop capable nilpotent groups
In this paper we consider finite loops and discuss the problem which nilpotent groups are isomorphic to the inner mapping group of a loop. We recall some earlier results and by using connected transversals we transform the problem into a group theoretical one. We will get some new answers as we show that a nilpotent group having either , as the Sylow -subgroup for some odd prime or the group of quaternions as the Sylow -subgroup may not be loop capable.
On the total number of principal series of a finite abelian group.
OnCSQ-normal subgroups of finite groups
We introduce a new subgroup embedding property of finite groups called CSQ-normality of subgroups. Using this subgroup property, we determine the structure of finite groups with some CSQ-normal subgroups of Sylow subgroups. As an application of our results, some recent results are generalized.
-groups, diagonalizable automorphisms and loops
Parallelepipeds, nilpotent groups and Gowers norms
In his proof of Szemerédi’s Theorem, Gowers introduced certain norms that are defined on a parallelepiped structure. A natural question is on which sets a parallelepiped structure (and thus a Gowers norm) can be defined. We focus on dimensions and and show when this possible, and describe a correspondence between the parallelepiped structures and nilpotent groups.
Permutable Subgroups of Infinite Groups.
p-Nilpotence, classifying space indecomposability, and other properties of almost all finite groups.
Principalization algorithm via class group structure
For an algebraic number field with -class group of type , the structure of the -class groups of the four unramified cyclic cubic extension fields , , of is calculated with the aid of presentations for the metabelian Galois group of the second Hilbert -class field of . In the case of a quadratic base field it is shown that the structure of the -class groups of the four -fields frequently determines the type of principalization of the -class group of in . This provides...
Products of finite nilpotent groups.