scholarly journals A note on locally soluble, normal closures of cyclic subgroups

1994 ◽  
Vol 36 (1) ◽  
pp. 33-36
Author(s):  
Howard Smith
Keyword(s):  
Normal Closure ◽  
Cyclic Subgroups ◽  
Rank Restrictions ◽  
Background Material ◽  
Derived Series ◽  
Usual Notation

This brief note has the threefold purpose of improving on an earlier theorem of the author [4], gathering together some results on normal closures (with rank restrictions) which are more or less implicit in the literature and providing a few examples which indicate the impossibility of improving these results in one way or another. The proofs are mostly routine and usually omitted. Most of the relevant background material can be found in [3], and references to these results will often indicate that minoradditional details (an easy induction, for example) are required. Throughout, 〈x〉G will denote the normal closure of the subgroup 〈x〉 of the group G. The usual notation is used for upper central and derived series.

FINITE p-GROUPS IN WHICH THE NORMAL CLOSURES OF THE NON-NORMAL CYCLIC SUBGROUPS HAVE SMALL INDEX

2013 ◽  
Vol 13 (02) ◽  
pp. 1350087 ◽  
Author(s):  
LIBO ZHAO ◽  
XIUYUN GUO
Keyword(s):  
Cyclic Subgroup ◽  
Normal Closure ◽  
Cyclic Subgroups ◽  
Small Index

A p-group is called a C(pw)-group if the normal closure of every non-normal cyclic subgroup has index at most pw. In this paper, we prove that the order of a non-Dedekind C(pw)-group cannot exceed p4w+4 when p > 2 and G′ ≤ HG for every non-normal cyclic subgroup H. We also completely classify non-Dedekind C(p2)-groups for p > 2.

Finite Groups with Small Normal Closure of Cyclic Subgroups

2014 ◽  
Vol 42 (11) ◽  
pp. 4984-4996 ◽  
Author(s):  
Heng Lv ◽  
Wei Zhou ◽  
Xiuyun Guo
Keyword(s):  
Finite Groups ◽  
Normal Closure ◽  
Cyclic Subgroups

Preliminaries

2017 ◽  
Author(s):  
Ehud Hrushovski ◽  
François Loeser
Keyword(s):  
Valued Fields ◽  
Definable Set ◽  
Valued Field ◽  
Galois Coverings ◽  
Definable Type ◽  
Definable Sets ◽  
Background Material

This chapter provides some background material on definable sets, definable types, orthogonality to a definable set, and stable domination, especially in the valued field context. It considers more specifically these concepts in the framework of the theory ACVF of algebraically closed valued fields and describes the definable types concentrating on a stable definable V as an ind-definable set. It also proves a key result that demonstrates definable types as integrals of stably dominated types along some definable type on the value group sort. Finally, it discusses the notion of pseudo-Galois coverings. Every nonempty definable set over an algebraically closed substructure of a model of ACVF extends to a definable type.

On 4-Engel Groups

2007 ◽  
Vol 10 ◽  
pp. 341-353 ◽  
Author(s):  
Michael Vaughan-Lee
Keyword(s):  
Normal Closure ◽  
Engel Group

In this note, the author proves that a group G is a 4-Engel group if and only if the normal closure of every element g ∈ G is a 3-Engel group

Integrability: From Statistical Systems to Gauge Theory

2019 ◽  
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Summer School ◽  
Condensed Matter ◽  
Theoretical Physics ◽  
Conformal Field ◽  
The Past ◽  
Background Material ◽  
Supersymmetric Gauge ◽  
Statistical Systems

This volume contains lectures delivered at the Les Houches Summer School ‘Integrability: from statistical systems to gauge theory’ held in June 2016. The School was focussed on applications of integrability to supersymmetric gauge and string theory, a subject of high and increasing interest in the mathematical and theoretical physics communities over the past decade. Relevant background material was also covered, with lecture series introducing the main concepts and techniques relevant to modern approaches to integrability, conformal field theory, scattering amplitudes, and gauge/string duality. The book will be useful not only to those working directly on integrablility in string and guage theories, but also to researchers in related areas of condensed matter physics and statistical mechanics.

scholarly journals On the sandpile model of modified wheels II

2020 ◽  
Vol 18 (1) ◽  
pp. 1531-1539
Author(s):  
Zahid Raza ◽  
Mohammed M. M. Jaradat ◽  
Mohammed S. Bataineh ◽  
Faiz Ullah
Keyword(s):  
Direct Product ◽  
Critical Group ◽  
Complete Structure ◽  
Sandpile Model ◽  
Cyclic Subgroups ◽  
Algebr Comb ◽  
Abelian Sandpile ◽  
Chip Firing ◽  
Sandpile Group

Abstract We investigate the abelian sandpile group on modified wheels {\hat{W}}_{n} by using a variant of the dollar game as described in [N. L. Biggs, Chip-Firing and the critical group of a graph, J. Algebr. Comb. 9 (1999), 25–45]. The complete structure of the sandpile group on a class of graphs is given in this paper. In particular, it is shown that the sandpile group on {\hat{W}}_{n} is a direct product of two cyclic subgroups generated by some special configurations. More precisely, the sandpile group on {\hat{W}}_{n} is the direct product of two cyclic subgroups of order {a}_{n} and 3{a}_{n} for n even and of order {a}_{n} and 2{a}_{n} for n odd, respectively.

scholarly journals The Pauli–Jung Conjecture and Its Relatives: A Formally Augmented Outline

2020 ◽  
Vol 3 (1) ◽  
pp. 527-549
Author(s):  
Harald Atmanspacher
Keyword(s):  
20Th Century ◽  
General Framework ◽  
Verbal Description ◽  
Main Body ◽  
Background Material ◽  
The Mind ◽  
Cross Fertilization

AbstractThe dual-aspect monist conjecture launched by Pauli and Jung in the mid-20th century will be couched in somewhat formal terms to characterize it more concisely than by verbal description alone. After some background material situating the Pauli–Jung conjecture among other conceptual approaches to the mind–matter problem, the main body of this paper outlines its general framework of a basic psychophysically neutral reality with its derivative mental and physical aspects and the nature of the correlations that connect these aspects. Some related approaches are discussed to identify key similarities to and deviations from the Pauli–Jung framework that may be useful for cross-fertilization.

scholarly journals A NEW RAMPED PYROXIDATION/COMBUSTION FACILITY AT 14CHRONO, BELFAST: SETUP DESCRIPTION AND INITIAL RESULTS

Radiocarbon ◽  
2021 ◽  
pp. 1-14
Author(s):  
Evelyn M Keaveney ◽  
Gerard T Barrett ◽  
Kerry Allen ◽  
Paula J Reimer
Keyword(s):  
Bulk Material ◽  
Correction Method ◽  
Source Attribution ◽  
Radiocarbon Age ◽  
Targeted Analysis ◽  
Consensus Values ◽  
Background Material ◽  
Initial Results ◽  
Blank Correction ◽  
Good Agreement

ABSTRACT The Belfast Ramped Pyroxidation/Combustion (RPO/RC) facility was established at the 14CHRONO Centre (Queen’s University Belfast). The facility was created to provide targeted analysis of bulk material for refined chronological analysis and carbon source attribution for a range of sample types. Here we report initial RPO results, principally on background material, but also including secondary standards that are routinely analyzed at 14CHRONO. A description of our setup, methodology, and background (blank) correction method for the system are provided. The backgrounds (anthracite, spar calcite, Pargas marble) reported by the system are in excess of 35,000 14C years BP with a mean age of 39,345 14C years BP (1σ = 36,497–43,800 years BP, N=44) with F14C = 0.0075 ± 0.0032. Initial results for standards are also in good agreement with consensus values: TIRI-B pine radiocarbon age = 4482 ± 47 years BP (N=13, consensus = 4508 years BP); IAEA-C6 ANU Sucrose F14C= 1.5036 ± 0.0034 (N=10, consensus F14C = 1.503). These initial tests have allowed problematic issues to be identified and improvements made for future analyses.

Hereditary polyneuropathy in the Alaskan Malamute

2012 ◽  
Vol 40 (01) ◽  
pp. 26-34 ◽  
Author(s):  
T. Bilzer ◽  
S. Petri ◽  
G. Schanen ◽  
M. Fehr ◽  
O. Distl ◽  
...  
Keyword(s):  
Segregation Analysis ◽  
Nerve Conduction Velocity ◽  
Axonal Degeneration ◽  
Phenotypic Expression ◽  
Disease Status ◽  
Nerve Biopsy ◽  
Hereditary Disease ◽  
Genetic Transmission ◽  
Clinically Normal ◽  
Background Material

Summary Objective: To prove the hypothesis that a polyneuropathy in Alaskan Malamutes has a genetic background. Material and methods: Pedigrees of 131 related Alaskan Malamutes were included in the current study. Neurological examination, electrodiagnosis as well as muscle and nerve biopsies could be performed in 10 dogs. Information about the disease status of the other 121 Alaskan Malamutes were supplied by referring veterinarians, breeders and owners. Segregation analysis using four different models (monogenic, polygenic, mixed monogenicpolygenic and the phenotypic model) was performed on 71 dogs to test the different mechanisms of genetic transmission. Results: In seven clinically affected dogs abnormal electromyographic findings and reduced nerve conduction velocity were detected. Suspected diagnosis of polyneuropathy was confirmed by nerve biopsy results, characterized by axonal degeneration and hypomyelination. Muscle specimens revealed signs of neurogenic myopathy. Three related clinically normal Alaskan Malamutes also displayed moderate neuromuscular changes in histopathology. In the segregation analysis the polygenic model proved as best suitable to explain the observed segregation pattern among all other models tested. Conclusion: The current study could demonstrate that polyneuropathy in Alaskan Malamutes is a hereditary disease with variable phenotypic expression ranging from severely affected to subclinical forms, which has to be considered in future gene analysis studies.

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