Bang-Bang Extremals in Sub-Finsler Problems on Engel Group

In this paper we provide a characterization of Lie solvable group algebras of derived length three over a field of characteristic three when G is a non-2-Engel group with abelian commutator subgroup.

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A geometric inequality for stable solutions of semilinear elliptic problems in the Engel group

Annales Academiae Scientiarum Fennicae Mathematica ◽

10.5186/aasfm.2012.3733 ◽

2012 ◽

Vol 37 ◽

pp. 357-373 ◽

Cited By ~ 7

Author(s):

Andrea Pinamonti ◽

Enrico Valdinoci

Keyword(s):

Elliptic Problems ◽

Geometric Inequality ◽

Engel Group ◽

Semilinear Elliptic ◽

Semilinear Elliptic Problems ◽

Stable Solutions

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On three-Engel groups

Bulletin of the Australian Mathematical Society ◽

10.1017/s000497270004524x ◽

1972 ◽

Vol 7 (3) ◽

pp. 391-405 ◽

Cited By ~ 30

Author(s):

L.-C. Kappe ◽

W.P. Kappe

Keyword(s):

Nilpotency Class ◽

The Other ◽

Maximal Class ◽

Engel Group

The following conditions for a group G are investigated:(i) maximal class n subgroups are normal,(ii) normal closures of elements have nilpotency class n at most,(iii) normal closures are n–Engel groups,(iv) G is an (n+1 )-Engel group.Each of these conditions is a consequence of the preceding one. The second author has shown previously that all conditions are equivalent for n = 1. Here the question is settled for n = 2 as follows: conditions (ii), (iii) and (iv) are equivalent. The class of groups defined by (i) is not closed under homomorphisms, and hence (i) does not follow from the other conditions.

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Third Engel groups

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972700004329 ◽

1989 ◽

Vol 40 (2) ◽

pp. 215-230 ◽

Cited By ~ 10

Author(s):

N. D. Gupta ◽

M. F. Newman

Keyword(s):

Normal Form ◽

Lower Central Series ◽

Central Series ◽

Engel Group ◽

Form Theorem ◽

Normal Form Theorem ◽

Computer Calculations

We present some new results on third Engel groups which are motivated by computer calculations but are not dependent on them. They include:• for n > 2 every n-generator third Engel group is nilpotent of class at most 2n – 1;• the fifth term of the lower central series of a third Engel group has exponent dividing 20;• the subgroup generated by fifth powers of elements in a third Engel group is nearly centre-by-metabeliami;and a normal form theorem for freest third Engel groups without elements of order 2.

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Nonexistence Results for Semilinear Equations in Carnot Groups

Analysis and Geometry in Metric Spaces ◽

10.2478/agms-2013-0001 ◽

2013 ◽

Vol 1 ◽

pp. 130-146 ◽

Cited By ~ 5

Author(s):

Fausto Ferrari ◽

Andrea Pinamonti

Keyword(s):

Heisenberg Group ◽

Carnot Group ◽

Carnot Groups ◽

Semilinear Equations ◽

Engel Group ◽

Large Step

Abstract In this paper, following [3], we provide some nonexistence results for semilinear equations in the the class of Carnot groups of type ★.This class, see [20], contains, in particular, all groups of step 2; like the Heisenberg group, and also Carnot groups of arbitrarly large step. Moreover, we prove some nonexistence results for semilinear equations in the Engel group, which is the simplest Carnot group that is not of type ★.

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