Results 171 to 180 of about 9,591,284 (211)

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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A Criterion for a Group to be Nilpotent

Bulletin of the London Mathematical Society, 1992
Let \(G\) be a finite group. The character degree frequency \(m_ G: \mathbb{N} \to \mathbb{Z}\) is defined \(m_ G(n) = |\{\chi \in \text{Irr }G\mid\chi(1) = n\}|\) and the class size frequency function \(w_ G: \mathbb{N} \to \mathbb{Z}\) by \(w_ G(n) = (1/n)|\{g \in G\mid| G: C_ G(g)| = n\}|\) which is the number of conjugacy classes of \(G\) with \(n\)
Cossey, John, Hawkes, Trevor, Mann, Avinoam   +2 more
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Semivarieties of nilpotent groups

Algebra and Logic, 2010
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On constructive nilpotent groups

Siberian Mathematical Journal, 2007
Summary: We prove the following: (1) a torsion-free class 2 nilpotent group is constructivizable if and only if it is isomorphic to the extension of some constructive Abelian group included in the center of the group by some constructive torsion-free Abelian group and some recursive system of factors; (2) a constructivizable torsion-free class 2 ...
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Compressibility in Nilpotent Groups

Bulletin of the London Mathematical Society, 1985
A group G is compressible if whenever H is a subgroup of finite index in G there exists a copy of G of finite index in H. This paper explores this property in the class of torsion-free finitely generated nilpotent groups, and obtains a local/global theorem. The methods of pro-finite and pro-p completion are used.
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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.
openaire   +1 more source

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
openaire   +3 more sources

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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