Multicolored graphs on countable ordinals of finite exponent

2002 ◽  
pp. 31-43
Author(s):  
Carl Darby ◽  
Jean Larson
Keyword(s):  
Finite Exponent

scholarly journals Group Laws Implying Virtual Nilpotence

2003 ◽  
Vol 74 (3) ◽  
pp. 295-312 ◽  
Author(s):  
R. G. Burns ◽  
Yuri Medvedev
Keyword(s):  
Large Class ◽  
Finite Groups ◽  
Additional Condition ◽  
Metabelian Group ◽  
Nilpotency Class ◽  
Finitely Generated ◽  
Finitely Generated Groups ◽  
Locally Graded Groups ◽  
Finite Exponent ◽  
Group Law

AbstractIf ω ≡ 1 is a group law implying virtual nilpotence in every finitely generated metabelian group satisfying it, then it implies virtual nilpotence for the finitely generated groups of a large class of groups including all residually or locally soluble-or-finite groups. In fact the groups of satisfying such a law are all nilpotent-by-finite exponent where the nilpotency class and exponent in question are both bounded above in terms of the length of ω alone. This yields a dichotomy for words. Finally, if the law ω ≡ 1 satisfies a certain additional condition—obtaining in particular for any monoidal or Engel law—then the conclusion extends to the much larger class consisting of all ‘locally graded’ groups.

scholarly journals Criteria for Commutativity in Large Groups

1998 ◽  
Vol 41 (1) ◽  
pp. 65-70 ◽  
Author(s):  
A. Mohammadi Hassanabadi ◽  
Akbar Rhemtulla
Keyword(s):  
Abelian Group ◽  
List Type ◽  
Quaternion Group ◽  
Large Groups ◽  
Positive Integers ◽  
Finite Exponent

AbstractIn this paper we prove the following:1.Let m ≥ 2, n ≥ 1 be integers and let G be a group such that (XY)n = (YX)n for all subsets X, Y of size m in G. Thena)G is abelian or a BFC-group of finite exponent bounded by a function of m and n.b)If m ≥ n then G is abelian or |G| is bounded by a function of m and n.2.The only non-abelian group G such that (XY)2 = (YX)2 for all subsets X, Y of size 2 in G is the quaternion group of order 8.3.Let m, n be positive integers and G a group such that for all subsets Xi of size m in G. Then G is n-permutable or |G| is bounded by a function of m and n.

On reflexive group topologies on abelian groups of finite exponent

2012 ◽  
Vol 99 (6) ◽  
pp. 583-588 ◽  
Author(s):  
L. Außenhofer ◽  
S. S. Gabriyelyan
Keyword(s):  
Abelian Groups ◽  
Finite Exponent ◽  
Reflexive Group

scholarly journals On varieties of soluble groups II

1972 ◽  
Vol 7 (3) ◽  
pp. 437-441 ◽  
Author(s):  
J.R.J. Groves
Keyword(s):  
Nilpotent Group ◽  
Metabelian Groups ◽  
Locally Finite ◽  
Soluble Groups ◽  
Finite Exponent

It is shown that, in a variety which does not contain all metabelian groups and is contained in a product of (finitely many) varieties each of which is soluble or locally finite, every group is an extension of a group of finite exponent by a nilpotent group by a group of finite exponent.

Transformations preserving the Lyapunov exponents

2018 ◽  
Vol 20 (04) ◽  
pp. 1750027 ◽  
Author(s):  
Luis Barreira ◽  
Claudia Valls
Keyword(s):  
Lyapunov Exponents ◽  
Asymptotic Properties ◽  
Regular Sequence ◽  
Complete Characterization ◽  
Block Form ◽  
The Family ◽  
Coordinate Changes ◽  
Invertible Matrices ◽  
Finite Exponent

We give a complete characterization of the existence of Lyapunov coordinate changes bringing an invertible sequence of matrices to one in block form. In other words, we give a criterion for the block-trivialization of a nonautonomous dynamics with discrete time while preserving the asymptotic properties of the dynamics. We provide two nontrivial applications of this criterion: we show that any Lyapunov regular sequence of invertible matrices can be transformed by a Lyapunov coordinate change into a constant diagonal sequence; and we show that the family of all coordinate changes preserving simultaneously the Lyapunov exponents of all sequences of invertible matrices (with finite exponent) coincides with the family of Lyapunov coordinate changes.

À propos d'équations génériques

1992 ◽  
Vol 57 (2) ◽  
pp. 548-554 ◽  
Author(s):  
Frank O. Wagner
Keyword(s):  
Solvable Group ◽  
Finite Index ◽  
Stable Group ◽  
Finite Exponent

AbstractWe prove that a stable solvable group G which satisfies xn = 1 generically is of finite exponent dividing some power of n. Furthermore, G is nilpotent-by-finile.A second result is that in a stable group of finite exponent, involutions either have big centralisers, or invert a subgroup of finite index (which hence has to be abelian).

scholarly journals Groups of finite exponent

1975 ◽  
Vol 12 (1) ◽  
pp. 99-99 ◽  
Author(s):  
N.D. Gupta ◽  
M.F. Newman
Keyword(s):  
Negative Answer ◽  
Finitely Generated ◽  
Finitely Generated Group ◽  
Finite Exponent

The negative answer by Novikov and Adyan to the Burnside question (is every finitely generated group of finite exponent finite?) still leaves open some cases, in particular, all 2-power exponents. Some reduction results are known. In this note we present another kind of reduction result.

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