Results 1 to 10 of about 21,501,912 (352)
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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The conjugacy problem for ascending HNN‐extensions of free groups [PDF]
Proceedings of the London Mathematical Society, 2022 We give an algorithm to solve the Conjugacy Problem for ascending HNN‐extensions of free groups. To do this, we give algorithms to solve certain problems on dynamics of free group endomorphisms.
Alan D. Logan
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Onto extensions of free groups [PDF]
Groups, Complexity, Cryptology, 2021 An extension of subgroups $H\leqslant K\leqslant F_A$ of the free group of rank $|A|=r\geqslant 2$ is called onto when, for every ambient free basis $A'$, the Stallings graph $\Gamma_{A'}(K)$ is a quotient of $\Gamma_{A'}(H)$.
Sebastià Mijares, Enric Ventura
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Free Proalgebraic Groups [PDF]
Épijournal de Géométrie Algébrique, 2020 Replacing finite groups by linear algebraic groups, we study an algebraic-geometric counterpart of the theory of free profinite groups. In particular, we introduce free proalgebraic groups and characterize them in terms of embedding problems.
Michael Wibmer
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The Unipotency of the Free Group with Linear Representation of Dimension 9
Journal of Harbin University of Science and Technology, 2021 By using the method of combinatorial group theory, the properties of primitives are found. By discussing different Jordan canonical forms and analyzing the properties of unipotent matrices, and by using computer software, the conditions that binary ...
YANG Xin-song, DIAO Xin
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Groups with context-free Diophantine problem [PDF]
Groups, Complexity, Cryptology, 2021 We find algebraic conditions on a group equivalent to the position of its Diophantine problem in the Chomsky Hierarchy. In particular, we prove that a finitely generated group has a context-free Diophantine problem if and only if it is finite.
Vladimir Yankovskiy
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Non-∀-homogeneity in free groups
Bulletin of Mathematical Sciences, 2021 We prove that non-abelian free groups of finite rank at least 3 or of countable rank are not ∀-homogeneous. We answer three open questions from Kharlampovich, Myasnikov, and Sklinos regarding whether free groups, finitely generated elementary free groups,
Olga Kharlampovich, Christopher Natoli
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Free groups defined by finite $p$-automata
Researches in Mathematics, 2023 For every odd prime $p$ we construct two $p$-automata with 14 inner states and prove that the group generated by 2 automaton permutations defined at their states is a free group of rank 2.
A.P. Krenevych, A.S. Oliynyk
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Free products of cyclic groups in groups of infinite unitriangular matrices
Математичні Студії, 2023 Groups of infinite unitriangular matrices over associative unitary rings are considered. These groups naturally act on infinite dimensional free modules over underlying rings. They are profinite in case underlying rings are finite.
A. Oliynyk
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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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