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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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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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Energies, 2023 South African universities boast a remarkable solar photovoltaic (PV) resource as a primary renewable energy component. Due to high peak demand tariffs and inherent prominent heating and cooling loads, fast and granular demand response programs are well ...
Stephanus Erasmus +2 more
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Suicide epidemic in Malawi: what can we do?
The Pan African Medical Journal, 2021 Suicide continues to be a global health concern, affecting all continents. Although some studies have associated it with mental disorders such as severe depression, research also shows that a significant number of cases occur due to emerging life ...
Gift Treighcy Banda +3 more
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Tobacco Induced Diseases, 2018 Introduction Ege University is a pioneering university at Ege region with its 70 000 students and approximately 3000 academic staff. Tobacco control policies, parallel to the current regulations in the country, are an important issue for Ege University ...
Isil Ergin +15 more
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