Results 1 to 10 of about 3,616,669 (319)
About an Extension of the Mirsky-Newman, Davenport-Rado Result to the Herzog-Schönheim Conjecture for Free Groups [PDF]
Advances in Group Theory and Applications, 2021 Let G be a group and H1, ..., Hs be subgroups of G of indices d1, ..., ds respectively. In 1974, M. Herzog and J. Schönheim conjectured that if {H_i alpha_i}, alpha_i in G, is a coset partition of G, then d1, ..., ds cannot be distinct.
Fabienne Chouraqui
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The Unipotency of Linear Groups Generated by Matrices with No More than Five Jorden Blocks
Journal of Harbin University of Science and Technology, 2022 Aiming at the question whether the group generated by two unipotent matrices whose Jordan blocks are of order no more than five is a unipotent group, based on the fundamental definition of nilpotent matrix, we use the matrix logarithm tool to obtain some
YANG Xin-song, LI Jia-xin
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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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The Unipotency of the Free Group with Linear Representation of Dimension 11
Journal of Harbin University of Science and Technology, 2022 For the unipotent problem of binary-generated free groups, the new trace equations are obtained by intensive study of combinatorial properties of the primitive element of the binary-generated free groups.
YANG Xin-song, XIA Xiao-dan
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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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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 Number of Sides of a Parallelogram [PDF]
Discrete Mathematics & Theoretical Computer Science, 1999 We define parallelograms of base a and b in a group. They appear as minimal relators in a presentation of a subgroup with generators a and b. In a Lie group they are realized as closed polygonal lines, with sides being orbits of left-invariant vector ...
Elisha Falbel, Pierre-Vincent Koseleff
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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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Journal of Fungi, 2021 Severe cases of coronavirus disease 2019 (COVID-19) managed in the intensive care unit are prone to complications, including secondary infections with opportunistic fungal pathogens.
Obinna T. Ezeokoli +2 more
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Measuring cones and other thick subsets in free groups [PDF]
International Journal of Group Theory, 2018 In this paper we investigate the special automata over finite rank free groups and estimate asymptotic characteristics of sets they accept. We show how one can decompose an arbitrary regular subset of a finite rank free group into disjoint union of ...
Elizaveta Frenkel +1 more
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