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Let $G$ be a group and $m$ be an integer greater than or equal to $2$ . $G$ is said to be $m$ -permutable if every product of $m$ elements can be reordered at least in one way. We prove that, if $G$ has a centre of finite index $z$ , then $G$ is $(1+[z/2])$ -permutable. More bounds are given on the least $m$ such that $G$ is $m$ -permutable.

Powers of a product of commutators as products of squares.

Abdollahi, Alireza (2004)

International Journal of Mathematics and Mathematical Sciences

Powers of commutators as products of squares.

Akhavan-Malayeri, M. (2002)

International Journal of Mathematics and Mathematical Sciences

Quelques bases et familles basiques des algèbres de Lie libres commodes pour les calculs sur ordinateurs

Gerard Viennot (1977)

Mémoires de la Société Mathématique de France

Reduced Forms for Quadratic Words and Spines of 2-manifolds.

E.C. Turner, R.Z. Goldstein (1981)

Mathematische Zeitschrift

Relative commutator associated with varieties of $n$ -nilpotent and of $n$ -solvable groups

Tomas Everaert, Marino Gran (2006)

Archivum Mathematicum

In this note we determine explicit formulas for the relative commutator of groups with respect to the subvarieties of $n$ -nilpotent groups and of $n$ -solvable groups. In particular these formulas give a characterization of the extensions of groups that are central relatively to these subvarieties.

Some conditions implying that an infinite group is abelian

Luise-Charlotte Kappe, M. J. Tomkinson (1998)

Rendiconti del Seminario Matematico della Università di Padova

Some conditions on infinite subsets of infinite groups.

Abdollahi, Alireza, Taeri, Bijan (1999)

Bulletin of the Malaysian Mathematical Society. Second Series

Some group theoretic problems inspired by ring theoretic analogies.

Pálfy, Péter P., Steinfeld, Ottó (2002)

Mathematica Pannonica

Su di un problema combinatorio in teoria dei gruppi

Mario Curzio, Patrizia Longobardi, Mercede Maj (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Let $G$ be a group and $n$ an integer $\geq 2$ . We say that $G$ has the $n$ -permutation property $(G\in P_{n})$ if, for any elements $x_{1},x_{2},\cdots,x_{n}$ in $G$ , there exists some permutation $\sigma$ of $\{1,2,\cdots,n\}$ , $\sigma\neq id.$ such that $x_{1},x_{2},\cdots,x_{n}=x_{\sigma(1)},x_{\sigma(2)},\cdots,x_{\sigma(n)}$ . We prouve that every group $G\in P_{n}$ is an FC-nilpotent group of class $\leq n-1$ , and that a finitely generated group has the $n$ -permutation property (for some $n$ ) if, and only if, it is abelian by finite. We prouve also that a group $G\in P_{3}$ if, and only if, its derived subgroup has order at most 2.

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On the inverse limit of free nilpotent groups.

On the power-commutative kernel of locally nilpotent groups.

On variants of a theorem of Schur.

Permutability of centre-by-finite groups

Powers of a product of commutators as products of squares.

Powers of commutators as products of squares.

Quelques bases et familles basiques des algèbres de Lie libres commodes pour les calculs sur ordinateurs

Reduced Forms for Quadratic Words and Spines of 2-manifolds.

Relative commutator associated with varieties of $n$ -nilpotent and of $n$ -solvable groups

Some conditions implying that an infinite group is abelian

Some conditions on infinite subsets of infinite groups.

Some group theoretic problems inspired by ring theoretic analogies.

Su di un problema combinatorio in teoria dei gruppi

Subgroups of Finite Index in Profinite Groups.

The classification of groups in which every product of four elements can be reordered

The Engel length of the product of Engel elements.

The equation $x^{2} y^{2} = g$ in partially commutative groups.

The equation $[x, y] = g$ in partially commutative groups.

The genus problem for one-relator products of locally indicable groups.

The lower central series of the free partially commutative group.

Currently displaying 41 – 60 of 82