1,720,958 research outputs found
On finitely generated Engel branch groups
No full textPetschick JM. On finitely generated Engel branch groups. Journal of the London Mathematical Society . 2024;110(3): e12980.We construct finitely generated Engel branch groups, answering a question of Fern & aacute;ndez-Alcober, Noce and Tracey on the existence of such objects. In particular, the groups constructed are not nilpotent, yielding the second known class of examples of finitely generated non-nilpotent Engel groups following a construction by Golod from 1969. To do so, we exhibit groups acting on rooted trees with growing valency on which word lengths of elements are contracting very quickly under section maps. Our methods apply in principle to a wider class of iterated identities, of which the Engel words are a special case
On finitely generated Engel branch groups
Full text linkWe construct finitely generated Engel branch groups, answering a question of
Fern\'andez-Alcober, Noce and Tracey on the existence of such objects. In
particular, the groups constructed are not nilpotent, yielding the second known
class of examples of finitely generated non-nilpotent Engel groups following a
construction by Golod from 1969. To do so, we exhibit groups acting on rooted
trees with growing valency on which word lengths of elements are contracting
very quickly under section maps. Our methods apply in principle to a wider
class of iterated identities, of which the Engel words are only a special case.Comment: 21 pages. Comments welcome! v2: Minor revisions in the exposition.
Clarification of Lemma 3.1
The derived series of GGS-groups
Full text linkGiven a GGS-group with non-constant defining tuple over a prime-regular
rooted tree, we calculate the indices and describe the structure
of the higher derived subgroups for all . We find
that the values depend only mildly on the structure of the
defining tuple.Comment: 20 pages. Version 2 contains a correction to the statement of Theorem
1.
Groups acting on rooted trees, the generalised Magnus property and zeta functions of groups
No full textCorrection: Conciseness of first-order formulae (Oct, 10.1007/s00605-025-02127-5, 2025)
No full textConte M, Petschick JM. Correction: Conciseness of first-order formulae (Oct, 10.1007/s00605-025-02127-5, 2025). Monatshefte für Mathematik. 2025.In the original version of this article, the author’s name J. Moritz Petschick was incorrectly written as MartinaJ. Moritz Petschick.
The original article has been corrected
On the Basilica operation
No full textPetschick JM, Rajeev K. On the Basilica operation. Groups, Geometry, and Dynamics. 2023;17(1):331-384.Inspired by the Basilica group B, we describe a general construction which allows us to associate to any group of automorphisms G < Aut(T ) of a rooted tree T a family of Basilica groups Bass(G), s E NC. For the dyadic odometer O2, one has B = Bas2(O2). We study which properties of groups acting on rooted trees are preserved under this operation. Introducing some techniques for handling Bass(G), in case G fulfills some branching conditions, we are able to calculate the Hausdorff dimension of the Basilica groups associated to certain GGS-groups and of generalisations of the odometer, Odm. Furthermore, we study the structure of groups of type Bass(Odm) and prove an analogue of the congruence subgroup property in the case m = p, a prime
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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