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Zeitschriftenartikel:

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.



Kurzfassung deutsch:
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

Kurzfassung englisch:
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

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


"Offizielle" elektronische Version der Publikation (entsprechend ihrem Digital Object Identifier - DOI)
http://dx.doi.org/10.31390/cosa.10.4.09


Erstellt aus der Publikationsdatenbank der Technischen Universität Wien.