University of IsfahanInternational Journal of Group Theory2251-765012320230901Minimal determining sets for certain $W$-graph ideals1231512649710.22108/ijgt.2022.131838.1764ENThomas P.McDonoughDepartment of Mathematics, Aberystwyth University, Aberystwyth SY23 3BZ, United KingdomChristos A.PallikarosDepartment of Mathematics and Statistics, University of Cyprus, P.O.Box 20537, 1678 Nicosia, CyprusJournal Article20211212We consider Kazhdan-Lusztig cells of the symmetric group $S_n$ containing the longest element of a standard parabolic subgroup of $S_n$. Extending some of the ideas in [Beiträge zur Algebra und Geometrie, <strong>59</strong> (2018) no.~3 523--547] and [Journal of Algebra and Its Applications, <strong>20</strong> (2021) no.~10 2150181], we determine the rim of some additional families of cells and also of certain induced unions of cells. These rims provide minimal determining sets for certain $W$-graph ideals introduced in [Journal of Algebra, <strong>361</strong> (2012) 188--212].https://ijgt.ui.ac.ir/article_26497_78e39e4495750d6909ab1b7562760b55.pdfUniversity of IsfahanInternational Journal of Group Theory2251-765012320230901On some new developments in the theory of subgroup lattices of groups1531622661810.22108/ijgt.2022.132076.1771ENMariaDe FalcoDipartimento di Matematica e Applicazioni, Università di Napoli Federico II Napoli, ItalyCarmelaMusellaDipartimento di Matematica e Applicazioni, Università di Napoli Federico II Napoli, ItalyJournal Article20211229A rather natural way for trying to obtain a lattice-theoretic characterization of a class of groups ${\mathcal X}$ is to replace the concepts appearing in the definition of ${\mathcal X}$ by lattice-theoretic concepts. The first to use this idea were Kontorovi\v{c} and Plotkin who in 1954 introduced the notion of modular chain in a lattice, as translation of a central series of a group, to determine a lattice-theoretic characterization of the class of torsion-free nilpotent groups. The aim of this paper is to present a recent application of this translation method to some generalized nilpotency properties.https://ijgt.ui.ac.ir/article_26618_4fa5889b4b31542b0c65fb633b016ce6.pdfUniversity of IsfahanInternational Journal of Group Theory2251-765012320230901Irredundant families of maximal subgroups of finite solvable groups1631762662010.22108/ijgt.2022.130778.1751ENAgnieszkaStockaFaculty of Mathematics, University of Bialystok, Ciolkowskiego 1M, 15-245 Bialystok, PolandJournal Article20211004Let $\mathcal{M}$ be a family of maximal subgroups of a group $G.$ We say that $\mathcal{M}$ is irredundant if its intersection is not equal to the intersection of any proper subfamily of $\mathcal{M}$. The maximal dimension of $G$ is the maximal size of an irredundant family of maximal subgroups of $G$. In this paper we study a class of solvable groups, called $\mathcal{M}$-groups, in which the maximal dimension has properties analogous to that of the dimension of a vector space such as the span property, the extension property and the basis exchange property.https://ijgt.ui.ac.ir/article_26620_64963867053680d71eab444f3ff10382.pdfUniversity of IsfahanInternational Journal of Group Theory2251-765012320230901A survey on the group of points arising from elliptic curves with a Weierstrass model over a ring1771962666510.22108/ijgt.2022.131984.1769ENMassimilianoSalaDepartment of Mathematics, University of Trento, Trento, Italy0000-0002-7266-5146DanieleTauferCISPA, Helmholtz Center for Information Security, Saarbrücken, Germany0000-0003-3402-4863Journal Article20211223We survey the known group structures arising from elliptic curves defined by Weierstrass models over commutative rings with unity and satisfying a technical condition. For every considered base ring, the groups that may arise depending on the curve coefficients are recalled. When a complete classification is still out of reach, partial results about the group structure and relevant subgroups are provided. Several examples of elliptic curves over the inspected rings are presented, and open questions regarding the structure of their points are highlighted.https://ijgt.ui.ac.ir/article_26665_eef610da29551cc3b348a913071109b3.pdfUniversity of IsfahanInternational Journal of Group Theory2251-765012320230901A Cheeger-Buser-type inequality on CW complexes1972042673010.22108/ijgt.2022.132100.1773ENGrégoireSchneebergerSection de matématiques, University of Geneva0000-0002-3431-4062Journal Article20211231We extend the definition of boundary expansion to CW complexes and prove a Cheeger-Buser-type relation between the spectral gap of the Laplacian and the boundary expansion of an orientable CW complex.https://ijgt.ui.ac.ir/article_26730_4a55b596ed83e4d63eebd663ec913a8e.pdfUniversity of IsfahanInternational Journal of Group Theory2251-765012320230901Finite coverings of semigroups and related structures2052222675010.22108/ijgt.2022.131538.1759ENCasey R.DonovenDepartment of Mathematics, Montana State University, Havre, MT, 59501, USA0000-0002-3685-0045Luise-CharlotteKappeDepartment of Mathematical Sciences, Binghamton University, Binghamton, NY, 13902-6000, USAJournal Article20211119For a semigroup $S$, the covering number of $S$ with respect to semigroups, $\sigma_s(S)$, is the minimum number of proper subsemigroups of $S$ whose union is $S$. This article investigates covering numbers of semigroups and analogously defined covering numbers of inverse semigroups and monoids. Our three main theorems give a complete description of the covering number of finite semigroups, finite inverse semigroups, and monoids (modulo groups and infinite semigroups). For a finite semigroup that is neither monogenic nor a group, its covering number is two. For all $n\geq 2$, there exists an inverse semigroup with covering number $n$, similar to the case of loops. Finally, a monoid that is neither a group nor a semigroup with an identity adjoined has covering number two as well.https://ijgt.ui.ac.ir/article_26750_d18569ae4418178d499f00b8dc03e96e.pdf