scholarly journals On the embedding problem for $2^+S_4$ representations

2007 ◽  
Vol 76 (260) ◽  
pp. 2063-2076
Author(s):  
Ariel Pacetti
Keyword(s):  
Embedding Problem

scholarly journals A note on embeddings for the Augmented Lagrange Method

2010 ◽  
Vol 20 (2) ◽  
pp. 183-196 ◽  
Author(s):  
Gemayqzel Bouza-Allende ◽  
Jurgen Guddat
Keyword(s):  
Augmented Lagrangian ◽  
Equality Constraints ◽  
Embedding Problem ◽  
Lagrange Method ◽  
Parametric Problem ◽  
Nonlinear Programs ◽  
Augmented Lagrange Method ◽  
Quadratic Perturbation ◽  
Lagrangian Embedding

Nonlinear programs (P) can be solved by embedding problem P into one parametric problem P(t), where P(1) and P are equivalent and P(0), has an evident solution. Some embeddings fulfill that the solutions of the corresponding problem P(t) can be interpreted as the points computed by the Augmented Lagrange Method on P. In this paper we study the Augmented Lagrangian embedding proposed in [6]. Roughly speaking, we investigated the properties of the solutions of P(t) for generic nonlinear programs P with equality constraints and the characterization of P(t) for almost every quadratic perturbation on the objective function of P and linear on the functions defining the equality constraints.

On the embedding problem with non-Abelian kernel of orderp 4. IV

1997 ◽  
Vol 83 (5) ◽  
pp. 637-641
Author(s):  
V. V. Ishkhanov ◽  
B. B. Lur'e
Keyword(s):  
Embedding Problem ◽  
Abelian Kernel

On normal subgroups of M-groups

2019 ◽  
Vol 18 (04) ◽  
pp. 1950074
Author(s):  
Xuewu Chang
Keyword(s):  
Normal Subgroup ◽  
Solvable Group ◽  
Solvable Groups ◽  
Hall Subgroup ◽  
Embedding Theorem ◽  
The Other ◽  
Finite Solvable Group ◽  
Embedding Problem ◽  
Normal Subgroups ◽  
Other Hand

The normal embedding problem of finite solvable groups into [Formula: see text]-groups was studied. It was proved that for a finite solvable group [Formula: see text], if [Formula: see text] has a special normal nilpotent Hall subgroup, then [Formula: see text] cannot be a normal subgroup of any [Formula: see text]-group; on the other hand, if [Formula: see text] has a maximal normal subgroup which is an [Formula: see text]-group, then [Formula: see text] can occur as a normal subgroup of an [Formula: see text]-group under some suitable conditions. The results generalize the normal embedding theorem on solvable minimal non-[Formula: see text]-groups to arbitrary [Formula: see text]-groups due to van der Waall, and also cover the famous counterexample given by Dade and van der Waall independently to the Dornhoff’s conjecture which states that normal subgroups of arbitrary [Formula: see text]-groups must be [Formula: see text]-groups.

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