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Powerful 2-Engel Groups
We study powerful 2-Engel groups. We show that every powerful 2-Engel group generated by three elements is nilpotent of class at most two. Surprisingly, the result does not hold when the number of generators is larger than...
On (n+1/2)-Engel groups
Let n be a positive integer. We say that a group G is an (n+1/2)-Engel group if it satisfies the law [ x, y n, x ] = 1. The variety of (n+1/2)-Engel groups lies between the varieties of n-Engel groups and (n+1) -Engel groups. In...
Powerful 2-Engel Groups
We study powerful 2-Engel groups. We show that every powerful 2-Engel group generated by three elements is nilpotent of class at most two. Surprisingly, the result does not hold when the number of generators is larger than...
On (n+1/2)-Engel groups
Let n be a positive integer. We say that a group G is an (n+1/2)-Engel group if it satisfies the law [ x, y n, x ] = 1. The variety of (n+1/2)-Engel groups lies between the varieties of n-Engel groups and (n+1) -Engel groups. In...
Right Engel-type subgroups and length parameters of finite groups
Let be an element of a finite group and let be the subgroup generated by all the right Engel values over. In the case when is soluble we prove that if, for some, the Fitting height of is equal to, then belongs to the th...
Powerful 2-Engel groups II
Gunnar Traustason
Jan 01, 0001
We conclude our classification of powerful 2-Engel groups of class three that are minimal in the sense that every proper powerful section is nilpotent of class at most two. In the predecessor to this paper we obtained three...
A note on conciseness of Engel words
It is still an open problem to determine whether the n-th Engel word [x,_n y] is concise, that is, if for every group G such that the set of values e_n(G) taken by [x,_n y] on G is finite it follows that the verbal subgroup...
Left 3-Engel elements in groups of exponent 5
G Traustason
Sep 15, 2014
It is still an open question whether a left 3-Engel element of a group G is always contained in the Hirsch–Plotkin radical of G. In this paper we begin a systematic study of this problem. The problem is first rephrased as saying...
A note on conciseness of Engel words
It is still an open problem to determine whether the n-th Engel word [x,_n y] is concise, that is, if for every group G such that the set of values e_n(G) taken by [x,_n y] on G is finite it follows that the verbal subgroup...
Right Engel-type subgroups and length parameters of finite groups
Let be an element of a finite group and let be the subgroup generated by all the right Engel values over. In the case when is soluble we prove that if, for some, the Fitting height of is equal to, then belongs to the th...
On the structure of right 3-Engel subgroups
Peter G Crosby
Apr 01, 2012
We state and prove two sharp results on the structure of normal subgroups consisting of right 3-Engel elements. First we prove that if H is a 3-torsion-free such subgroup of a group G and x ∈ G, then [H, 4〈 x 〉 G] = {1}. When H...
Powerful 2-Engel groups II
Gunnar Traustason
Jan 01, 0001
We conclude our classification of powerful 2-Engel groups of class three that are minimal in the sense that every proper powerful section is nilpotent of class at most two. In the predecessor to this paper we obtained three...
Left 3-Engel elements in groups of exponent 60
Let G be a group and let x G be a left 3-Engel element of order dividing 60. Suppose furthermore that (x)G has no elements of order 8, 9 and 25. We show that x is then contained in the locally nilpotent radical of G. In...
Left 3-Engel elements in groups of exponent 60
Let G be a group and let x G be a left 3-Engel element of order dividing 60. Suppose furthermore that (x)G has no elements of order 8, 9 and 25. We show that x is then contained in the locally nilpotent radical of G. In...
Normal right Engel subgroups of compact Hausdorff groups
Gunnar Traustason
Nov 15, 2014
Let G be a finitely generated compact Hausdorff topological group and let H be a closed normal subgroup consisting of right Engel elements. We show that H belongs to some term of the upper central series of G.
Left 3-Engel elements in groups of exponent 5
G Traustason
Sep 15, 2014
It is still an open question whether a left 3-Engel element of a group G is always contained in the Hirsch–Plotkin radical of G. In this paper we begin a systematic study of this problem. The problem is first rephrased as saying...
Sandwich groups and (strong) left 3-Engel elements in groups
In this paper we prove a group theoretic analogue of the well known local nilpotence theorem for sandwich Lie algebras due to Kostrikin and Zel’manov [Trudy Mat. Inst. Steklov. 183 (1990), pp. 106–111, 225]. We introduce the...
A left 3-Engel element whose normal closure is not nilpotent
We give an example of a locally nilpotent group G containing a left 3-Engel element x where 〈x〉 G is not nilpotent.
A left 3-Engel element whose normal closure is not nilpotent
We give an example of a locally nilpotent group G containing a left 3-Engel element x where 〈x〉 G is not nilpotent.
Sandwich groups and (strong) left 3-Engel elements in groups
In this paper we prove a group theoretic analogue of the well known local nilpotence theorem for sandwich Lie algebras due to Kostrikin and Zel’manov [Trudy Mat. Inst. Steklov. 183 (1990), pp. 106–111, 225]. We introduce the...
Normal right Engel subgroups of compact Hausdorff groups
Gunnar Traustason
Nov 15, 2014
Let G be a finitely generated compact Hausdorff topological group and let H be a closed normal subgroup consisting of right Engel elements. We show that H belongs to some term of the upper central series of G.
On the structure of right 3-Engel subgroups
Peter G Crosby
Apr 01, 2012
We state and prove two sharp results on the structure of normal subgroups consisting of right 3-Engel elements. First we prove that if H is a 3-torsion-free such subgroup of a group G and x ∈ G, then [H, 4〈 x 〉 G] = {1}. When H...
Friedrich Christoph Oetinger’s Speculative Pietism
Sean J. McGrath
Aug 29, 2018
The influence of Friedrich Christoph Oetinger (1702-82) on Schelling’s work is even deeper than that exerted by Jakob Boehme, deeper, not because Schelling devoted more scholarly attention to Oetinger than he did to the study of...
Published by: Memorial University Libraries
Friedrich Christoph Oetinger’s Speculative Pietism
Sean J. McGrath
Aug 29, 2018
The influence of Friedrich Christoph Oetinger (1702-82) on Schelling’s work is even deeper than that exerted by Jakob Boehme, deeper, not because Schelling devoted more scholarly attention to Oetinger than he did to the study of...
Published by: Memorial University Libraries
Open problems from the conference “engel conditions in groups” held in bath, UK, 2019
Gunnar Traustason
Dec 31, 2020
Here is list of open problems from the conference Engel Type Conditions in Groups in Bath that was held in April 2019.
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