4. Maximal Quasicentral Extensions, Maximal ℓ-Extensions and Maximal Class Two Extensions

1983 ◽  
pp. 45-60
Author(s):  
Albrecht Fröhlich
Keyword(s):  
Maximal Class

Centralizers of small order in p-groups of maximal class

1992 ◽  
Vol 20 (4) ◽  
pp. 1051-1059
Author(s):  
Antonio Vera-López ◽  
Gustavo A. Fernández-Alcober
Keyword(s):  
Maximal Class

scholarly journals Metabolomics of World Trade Center-Lung Injury: a machine learning approach

2018 ◽  
Vol 5 (1) ◽  
pp. e000274 ◽  
Author(s):  
George Crowley ◽  
Sophia Kwon ◽  
Syed Hissam Haider ◽  
Erin J Caraher ◽  
Rachel Lam ◽  
...  
Keyword(s):  
Machine Learning ◽  
Lung Function ◽  
Lung Injury ◽  
World Trade ◽  
World Trade Center ◽  
Forced Expiratory Volume ◽  
Machine Learning Techniques ◽  
Maximal Class ◽  
Class Separation ◽  
Trade Center

IntroductionBiomarkers of metabolic syndrome expressed soon after World Trade Center (WTC) exposure predict development of WTC Lung Injury (WTC-LI). The metabolome remains an untapped resource with potential to comprehensively characterise many aspects of WTC-LI. This case–control study identified a clinically relevant, robust subset of metabolic contributors of WTC-LI through comprehensive high-dimensional metabolic profiling and integration of machine learning techniques.MethodsNever-smoking, male, WTC-exposed firefighters with normal pre-9/11 lung function were segregated by post-9/11 lung function. Cases of WTC-LI (forced expiratory volume in 1s <lower limit of normal, n=15) and controls (n=15) were identified from previous cohorts. The metabolome of serum drawn within 6 months of 9/11 was quantified. Machine learning was used for dimension reduction to identify metabolites associated with WTC-LI.Results580 metabolites qualified for random forests (RF) analysis to identify a refined metabolite profile that yielded maximal class separation. RF of the refined profile correctly classified subjects with a 93.3% estimated success rate. 5 clusters of metabolites emerged within the refined profile. Prominent subpathways include known mediators of lung disease such as sphingolipids (elevated in cases of WTC-LI), and branched-chain amino acids (reduced in cases of WTC-LI). Principal component analysis of the refined profile explained 68.3% of variance in five components, demonstrating class separation.ConclusionAnalysis of the metabolome of WTC-exposed 9/11 rescue workers has identified biologically plausible pathways associated with loss of lung function. Since metabolites are proximal markers of disease processes, metabolites could capture the complexity of past exposures and better inform treatment. These pathways warrant further mechanistic research.

scholarly journals Graded Lie Algebras of Maximal Class

1997 ◽  
Vol 349 (10) ◽  
pp. 4021-4051 ◽  
Author(s):  
A. Caranti ◽  
S. Mattarei ◽  
M. F. Newman
Keyword(s):  
Lie Algebras ◽  
Maximal Class ◽  
Graded Lie Algebras

On the degree of commutativity of p-groups of maximal class

2011 ◽  
pp. 560-568
Author(s):  
A. Vera-López ◽  
M. A. García-Sánchez
Keyword(s):  
Maximal Class

ON p-GROUPS OF MAXIMAL CLASS II

1978 ◽  
Vol 29 (2) ◽  
pp. 175-186 ◽  
Author(s):  
C. R. LEEDHAM-GREEN ◽  
SUSAN McKAY
Keyword(s):  
Class Ii ◽  
Maximal Class

Finite p-groups with the least number of outer p-automorphisms

2017 ◽  
Vol 16 (06) ◽  
pp. 1750111
Author(s):  
Alireza Abdollahi ◽  
Marzieh Ahmadi ◽  
S. Mohsen Ghoraishi
Keyword(s):  
Nilpotency Class ◽  
Maximal Class ◽  
Frattini Subgroup ◽  
Special Cases

In this paper we study finite [Formula: see text]-groups [Formula: see text] for which the [Formula: see text]-part of [Formula: see text] has the least possible value [Formula: see text]. We characterize the groups in some special cases, including [Formula: see text]-groups of nilpotency class [Formula: see text], of maximal class, of order at most [Formula: see text], with cyclic Frattini subgroup and [Formula: see text]-groups [Formula: see text] in which [Formula: see text].

scholarly journals BOGOMOLOV MULTIPLIERS OF P-GROUPS OF MAXIMAL CLASS

2019 ◽  
Vol 71 (1) ◽  
pp. 123-138
Author(s):  
Gustavo A FernÁndez-Alcober ◽  
Urban Jezernik
Keyword(s):  
Lower Central Series ◽  
Maximal Class ◽  
Central Series ◽  
Natural Family ◽  
Positive Degree ◽  
Bogomolov Multiplier

Abstract Let $G$ be a $p$-group of maximal class and order $p^n$. We determine whether or not the Bogomolov multiplier ${\operatorname{B}}_0(G)$ is trivial in terms of the lower central series of $G$ and $P_1 = C_G(\gamma _2(G) / \gamma _4(G))$. If in addition $G$ has positive degree of commutativity and $P_1$ is metabelian, we show how understanding ${\operatorname{B}}_0(G)$ reduces to the simpler commutator structure of $P_1$. This result covers all $p$-groups of maximal class of large-enough order, and, furthermore, it allows us to give the first natural family of $p$-groups containing an abundance of groups with non-trivial Bogomolov multipliers. We also provide more general results on Bogomolov multipliers of $p$-groups of arbitrary coclass $r$.

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