Results 171 to 180 of about 5,393,663 (208)

ON ČERNIKOV-BY-NILPOTENT GROUPS

Journal of Algebra and Its Applications, 2006
In this paper, we study the class (Ω, ∞) of groups whose every infinite subset contains two distinct elements generating an Ω-group where Ω is either the class of Černikov groups, or the class of Černikov-by-nilpotent groups and we deduce some characterizations of finite-by-nilpotent groups.
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On a Property of Nilpotent Groups

Canadian Mathematical Bulletin, 1994
AbstractLet g be an element of a group G and [g, G] = 〈g-1a-1ga | a ∊ G〉. We prove that if G is locally nilpotent then for each g,t ∊ G either g[g, G] = t[t, G] or g[g, G] ∩ t[t, G] = Ø. The converse is true if G is finite.
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ON CERTAIN AUTOMORPHISMS OF NILPOTENT GROUPS

Mathematical Proceedings of the Royal Irish Academy, 2013
Let \(G\) be a group and \(\vartheta\in\Aut(G)\); the automorphism \(\vartheta\) is pointwise inner if \(\vartheta(g)\) is conjugate to \(g\) for every \(g\in G\) (that is \(\vartheta\) fixes the conjugacy classes of \(G\)). The set \(\Aut_{\mathrm{pwi}}(G)\) of pointwise inner automorphisms of \(G\) is a subgroup of \(\Aut(G)\) and obviously \(\mathrm{
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Nilpotent Covers of Dihedral Groups

Ars Combinatoria
Let G be a group, and let c ∈ Z + ∪ { ∞ } . We let σ c ( G ) be the maximal size of a subset X of G such that, for any distinct x 1 , x 2 ∈ X , the group ⟨ x 1 , x 2 ⟩ is not c -nilpotent; similarly we let Σ c ( G ) be the smallest number of c -nilpotent subgroups of G whose union is equal to G .
Kimeu Arphaxad Ngwava, Nick Gill
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Nilpotent Groups

1994
Abstract With the general theory of the previous chapter in hand, we can begin the structural analysis of groups of finite Morley rank. The general theory occupies Chapters 6 through 9. The present chapter deals with the structure theory for nilpotent groups.
Alexandre Borovik, Ali Nesin
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A (locally nilpotent)-by-nilpotent variety of groups

Mathematical Proceedings of the Cambridge Philosophical Society, 2002
Given positive integers k and n, let [Xfr ] be the class of all groups G such that γk(G) is locally nilpotent and [x1, x2, …, xk]n = 1 for any x1, x2, …, xk ∈ G. It is shown that [Xfr ] is a variety.
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Automorphism Groups of Nilpotent Groups

American Journal of Mathematics, 1969
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Nilpotent Topological Groups

Journal of the London Mathematical Society, 1973
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On a Class of Nilpotent Groups

Proceedings of the London Mathematical Society, 1960
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Second type nilpotent soft subgroups

Afrika Matematika, 2023
exaly