W. Herfort, K.H. Hofmann, F.G. Russo:

"A study in locally compact groups-Chabauty space, Sylow theory, the Schur-Zassenhaus formalism, the prime graph for near abelian group";

Communications on Stochastic Analysis (eingeladen),10(2016), 4; S. 515 - 540.

The class of

locally compact near abelian groups

is introduced

and investigated as a class of metabelian groups formalizing and applying

the concept of scalar multiplication. The structure of locally compact near

abelian groups and its close connections to prime number theory are discussed

and elucidated by graph theoretical tools. These investigations require a thor-

ough reviewing and extension to the present circumstances of various aspects

of the general theory of locally compact groups such as

-the Chabauty space of closed subgroups with its natural compact Hausdorff

topology,

-a very general Sylow subgroup theory for periodic groups including their

Hall systems,

-the scalar automorphisms of locally compact abelian groups,

-the theory of products of closed subgroups and their relation to semidirect

products, and

-inductively monothetic groups are introduced and classified.

As applications, firstly, a complete classification is given of

locally compact

topologically quasihamiltonian groups

, which has been initiated by F. K ̈um-

mich, and, secondly, Yu. Mukhin´s classification of

locally compact topologi-

cally modular groups

is retrieved and further illuminated

The class of

locally compact near abelian groups

is introduced

and investigated as a class of metabelian groups formalizing and applying

the concept of scalar multiplication. The structure of locally compact near

abelian groups and its close connections to prime number theory are discussed

and elucidated by graph theoretical tools. These investigations require a thor-

ough reviewing and extension to the present circumstances of various aspects

of the general theory of locally compact groups such as

-the Chabauty space of closed subgroups with its natural compact Hausdorff

topology,

-a very general Sylow subgroup theory for periodic groups including their

Hall systems,

-the scalar automorphisms of locally compact abelian groups,

-the theory of products of closed subgroups and their relation to semidirect

products, and

-inductively monothetic groups are introduced and classified.

As applications, firstly, a complete classification is given of

locally compact

topologically quasihamiltonian groups

, which has been initiated by F. K ̈um-

mich, and, secondly, Yu. Mukhin´s classification of

locally compact topologi-

cally modular groups

is retrieved and further illuminated

Locally Compact Group, Periodic Group, Metabelian, Quasihamiltonian, Lattice of Groups

http://dx.doi.org/10.31390/cosa.10.4.09

Erstellt aus der Publikationsdatenbank der Technischen Universität Wien.