Topological abelian groups with a Dedekind lattice of closed subgroups

Mukhin, Yu. N.

doi:10.1007/bf01104378

Cited by 3 publications

(12 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The endomorphism η : W → D ∩ U extends to a continuous homomorphism η : W + D → D which restricts to the identity on D. Therefore, setting R := ker( η) G = D ⊕ R is a splitting. Now we offer a new and short argument for the following result of Mukhin [10]. Proof.…”

Section: Some Consequencesmentioning

confidence: 94%

“…However, the class of topologically modular groups fails to be closed under the formation of strict projective limits and (local) products as the following example, due to Mukhin shows (see [10] which will be reproduced in Example 2.11 below). Example 2.10.…”

Section: Preliminariesmentioning

confidence: 99%

“…That inductively monothetic groups are always strongly topologically quasihamiltonian could be read off from Mukhin's characterization of abelian strongly topologically quasihamiltonian groups, see [10], a very elementary proof of this fact follows.…”

Section: Some Consequencesmentioning

confidence: 99%

“…Mukhin, see[10]). A locally compact abelian topologically modular p-group G satisfies one of the following conditions:(a) G contains an open compact subgroup of finite p-rank.…”

mentioning

confidence: 99%

See 3 more Smart Citations

When is the sum of two closed subgroups closed in a locally compact abelian group?

Herfort

Hofmann

Russo

2020

Topology and its Applications

View full text Add to dashboard Cite

show abstract

Section: Some Consequencesmentioning

confidence: 94%

Section: Preliminariesmentioning

confidence: 99%

Section: Some Consequencesmentioning

confidence: 99%

“…Mukhin, see[10]). A locally compact abelian topologically modular p-group G satisfies one of the following conditions:(a) G contains an open compact subgroup of finite p-rank.…”

mentioning

confidence: 99%

See 2 more Smart Citations

When is the sum of two closed subgroups closed in a locally compact abelian group?

Herfort

Hofmann

Russo

2020

Topology and its Applications

View full text Add to dashboard Cite

show abstract

“…Locally compact abelian topologically modular groups were classified by Mukhin in [37]. We now discuss the nonabelian situation.…”

Section: Application 2: the Classification Of Topologically Modular Gmentioning

confidence: 99%

A Study in Locally Compact Groups—Chabauty Space, Sylow Theory, the Schur-Zassenhaus Formalism, the Prime Graph for Near Abelian Groups

Herfort¹,

Hofmann²,

Russo³

2016

COSA

View full text Add to dashboard Cite

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 thorough reviewing and extension to 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. Kümmich, and, secondly, Yu. Mukhin's classification of locally compact topologically modular groups is retrieved and further illuminated.

show abstract

Some Lattice-Theoretical Properties of Groups and Semi-Groups

Arshinov¹,

Sadovskii²

1972

Russ. Math. Surv.

View full text Add to dashboard Cite

We derive an improved prescription for the merging of matrix elements with parton showers, extending the CKKW approach. A flavour-dependent phase space separation criterion is proposed. We show that this new method preserves the logarithmic accuracy of the shower, and that the original proposal can be derived from it. One of the main requirements for the method is a truncated shower algorithm. We outline the corresponding Monte Carlo procedures and apply the new prescription to QCD jet production in e + e − collisions and Drell-Yan lepton pair production. Explicit colour information from matrix elements obtained through colour sampling is incorporated in the merging and the influence of different prescriptions to assign colours in the large N C limit is studied. We assess the systematic uncertainties of the new method.

show abstract

Topological abelian groups with a Dedekind lattice of closed subgroups

Cited by 3 publications

References 2 publications

When is the sum of two closed subgroups closed in a locally compact abelian group?

When is the sum of two closed subgroups closed in a locally compact abelian group?

A Study in Locally Compact Groups—Chabauty Space, Sylow Theory, the Schur-Zassenhaus Formalism, the Prime Graph for Near Abelian Groups

Some Lattice-Theoretical Properties of Groups and Semi-Groups

Contact Info

Product

Resources

About