Results 1 to 10 of about 9,681,419 (157)
Free Boolean Topological Groups [PDF]
Axioms, 2015 Known and new results on free Boolean topological groups are collected. An account of the properties that these groups share with free or free Abelian topological groups and properties specific to free Boolean groups is given.
Ol’ga Sipacheva
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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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Transactions of the American Mathematical Society, 1986 In this paper we introduce the class of torsion free k k -groups and the notion of a knice subgroup. Torsion free k k -groups form a class of groups more extensive than the separable groups of Baer, but they enjoy many of the same closure properties.
Hill, Paul, Megibben, Charles
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Topology and its Applications, 2023 17 pages, 2 ...
Jeremy Brazas, Sarah Emery
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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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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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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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