Results 11 to 20 of about 9,725,411 (278)
Complexity of unification in free groups and free semi-groups [PDF]
Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science, 2002 It is proved that the exponent of periodicity of a minimal solution of a word equation is at most 2/sup 2.54n/, where n is the length of the equation. Since the best known lower bound is 2/sup 0.31n/, this upper bound is almost optimal and exponentially better than the original bound.
Antoni Koscielski, Leszek Pacholski
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The R ∞ property for free groups, free nilpotent groups and free solvable groups [PDF]
Bulletin of the London Mathematical Society, 2014 Let $F$ be either a free nilpotent group of a given class and of finite rank or a free solvable group of a certain derived length and of finite rank. We show precisely which ones have the $R_{\infty}$ property. Finally, we also show that the free group of infinite rank does not have the $R_{\infty}$ property.
Dekimpe, Karel, Gonçalves, Daciberg
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Free group automorphisms with parabolic boundary orbits [PDF]
, 2011 For $N\geq 4$, we show that there exist automorphisms of the free group $F_N$ which have a parabolic orbit in $\partial F_N$.
Arnaud Hilion, Ghys
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On one A.I. Mal’cev’s Question from the ”Kourovskaya Notebook”
Моделирование и анализ информационных систем, 2015 It is shown that the derived subgroup of the free group is not first-oder definable.
V. G. Durnev
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Journal of Knot Theory and Its Ramifications, 2010 Free knots are a simplification of virtual knots obtained by forgetting arrow/sign information at classical crossings. First non-trivial examples of free knots were constructed recently by the second named author. By using parity considerations, we construct invariants of free knots valued in certain groups.
Manturov V.O., Manturov O.V.
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The Axiomatics of Free Group Rings [PDF]
Groups, Complexity, Cryptology, 2021 In [FGRS1,FGRS2] the relationship between the universal and elementary theory of a group ring $R[G]$ and the corresponding universal and elementary theory of the associated group $G$ and ring $R$ was examined.
Benjamin Fine +4 more
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The automorphism group of the free group of rank two is a CAT(0) group [PDF]
, 2009 We prove that the automorphism group of the braid group on four strands acts faithfully and geometrically on a CAT(0) 2-complex. This implies that the automorphism group of the free group of rank two acts faithfully and geometrically on a CAT(0) 2 ...
Piggott, Adam +2 more
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AUTOMORPHISM GROUPS OF FREE GROUPS [PDF]
Journal of the Australian Mathematical Society, 2008 Abstract This note contains some remarks on generating pairs for automorphism groups of free groups. There has been significant use of electronic assistance. Little of this is used to verify the results.
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BMJ Open Respiratory Research, 2020 Background Obstructive sleep apnoea (OSA) presents a major healthcare challenge with current UK data suggesting that only 22% of individuals have been diagnosed and treated.
Stephanie K Mansell +5 more
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A non-trivial example of a free-by-free group with the Haagerup property [PDF]
, 2011 The aim of this note is to prove that the group of Formanek-Procesi acts properly isometrically on a finite dimensional CAT(0) cube complex. This gives a first example of a non-linear semidirect product between two non abelian free groups which satisfies
Gautero, François
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