Results 1 to 10 of about 7,806,548 (121)
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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New Zémor-Tillich Type Hash Functions Over GL2 (𝔽pn)
Journal of Mathematical Cryptology, 2020 We present a large class of new Zémor-Tillich type hash functions whose target space is the finite group GL2(𝔽pn) for any prime p and power n. To do so, we use a novel group-theoretic approach that uses Tits’ “Ping-Pong Lemma” to outline conditions under
Tomkins Hayley +2 more
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From mapping class groups to automorphism groups of free groups [PDF]
, 2005 We show that the natural map from the mapping class groups of surfaces to the automorphism groups of free groups, induces an infinite loop map on the classifying spaces of the stable groups after plus construction.
Wahl, Nathalie
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Annotation-free delineation of prokaryotic homology groups.
PLoS Computational Biology, 2022 Phylogenomic studies of prokaryotic taxa often assume conserved marker genes are homologous across their length. However, processes such as horizontal gene transfer or gene duplication and loss may disrupt this homology by recombining only parts of genes,
Yongze Yin, Huw A Ogilvie, Luay Nakhleh
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