On (λ, μ)-Classes on the 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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