University of IsfahanInternational Journal of Group Theory2251-765012420231201Solvable groups whose monomial, monolithic characters have prime power codegrees2232262628910.22108/ijgt.2022.131101.1755ENXiaoyouChenSchool of Sciences, Henan University of Technology, P.O.Box 450001, Zhengzhou, ChinaMark L.LewisDepartment of Mathematical Sciences, Kent State University, P.O.Box 44242, Kent, USAJournal Article20211019In this note, we prove that if $G$ is solvable and ${\rm cod}(\chi)$ is a $p$-power for every nonlinear, monomial, monolithic $\chi\in {\rm Irr}(G)$ or every nonlinear, monomial, monolithic $\chi \in {\rm IBr} (G)$, then $P$ is normal in $G$, where $p$ is a prime and $P$ is a Sylow $p$-subgroup of $G$.https://ijgt.ui.ac.ir/article_26289_47bc384bead7c28b76c6eff6dc178c60.pdfUniversity of IsfahanInternational Journal of Group Theory2251-765012420231201Trilinear alternating forms and related CMLs and GECs2272352635310.22108/ijgt.2022.131611.1760ENNoureddineMidouneDepartment of Mathematics, University of MSILA, P.O.Box 166, Msila, AlgeriaMohamed AnouarRakdiDepartment of Mathematics, University of MSILA, P.O.Box 166 Msila, AlgeriaJournal Article20211124The classification of trivectors(trilinear alternating forms) depends essentially on the dimension $n$ of the base space. This classification seems to be a difficult problem (unlike in the bilinear case). For $n\leq 8 $ there exist finitely many trivector classes under the action of the general linear group $GL(n).$ The methods of Galois cohomology can be used to determine the classes of nondegenerate trivectors which split into multiple classes when going from $\bar{K}$(the algebraic closure of $K$) to $K.$ In this paper, we are interested in the classification of trivectors of an eight dimensional vector space over a finite field of characteristic $3,$ $% K=\mathbb{F}_{3^{m}}.$ We obtain a $31$ inequivalent trivectors, $20$ of which are full rank. Having its motivation in the theory of the generalized elliptic curves and commutative moufang loop, this research studies the case of the forms over the 3 elements field. We use a transfer theorem providing a one-to-one correspondence between the classes of trilinear alternating forms of rank $8$ over a finite field with $3$ elements $\mathbb{F}_{3}$ and the rank $9$ class $2$ Hall generalized elliptic curves (GECs) of $3$-order $9$ and commutative moufang loop (CMLs). We derive a classification and explicit descriptions of the $31$ Hall GECs whose rank and $3$-order both equal $9$ and the number of order $3^{9}$-CMLs. https://ijgt.ui.ac.ir/article_26353_f99f3afe2da545dfb861114d76e0f418.pdfUniversity of IsfahanInternational Journal of Group Theory2251-765012420231201Ramification structures for quotients of multi-EGS groups2372522674910.22108/ijgt.2022.130522.1741ENElenaDi DomenicoDepartment of Mathematics, University of Trento, 38123, Trento, Italy - University of the Basque Country UPV/EHU,
48080, Bilbao, SpainŞükranGülDepartment of Mathematics, TED University, 06420, Ankara, Turkey0000-0003-4792-7084AnithaThillaisundaramCentre for Mathematical Sciences, Lund University, 223 62, Lund, SwedenJournal Article20210910Groups associated to surfaces isogenous to a higher product of curves can be characterised by a purely group-theoretic condition, which is the existence of a so-called ramification structure. Gül and Uria-Albizuri showed that quotients of the periodic Grigorchuk-Gupta-Sidki groups, GGS-groups for short, admit ramification structures. We extend their result by showing that quotients of generalisations of the GGS-groups, namely multi-EGS groups, also admit ramification structures.https://ijgt.ui.ac.ir/article_26749_21332b4d35737c46e841ce1355c647a0.pdfUniversity of IsfahanInternational Journal of Group Theory2251-765012420231201Profinite just infinite residually solvable Lie algebras2532642677210.22108/ijgt.2022.130053.1734ENDarioVillanis ZianiDepartment of Mathematics and Computer Science “U. Dini”, Università degli Studi di Firenze, viale Morgagni 67/A,
50134, Florence, Italy0000-0001-7826-2463Journal Article20210814We provide some characterization theorems about just infinite profinite residually solvable Lie algebras, similarly to what C. Reid has done for just infinite profinite groups. In particular, we prove that a profinite residually solvable Lie algebra is just infinite if and only if its obliquity subalgebra has finite codimension in the Lie algebra, and we establish a criterion for a profinite residually solvable Lie algebra to be just infinite, looking at the finite Lie algebras occurring in the inverse system.https://ijgt.ui.ac.ir/article_26772_2b33a31566f445730af689d7f9c7233b.pdfUniversity of IsfahanInternational Journal of Group Theory2251-765012420231201Remark on Laquer's theorem for circulant determinants2652692669810.22108/ijgt.2022.133217.1791ENNaoyaYamaguchiFaculty of Education, University of Miyazaki, Miyazaki, Japan0000-0003-4169-7409YukaYamaguchiFaculty of Education, University of Miyazaki, Miyazaki, Japan0000-0001-6226-4923Journal Article20220406Olga Taussky-Todd suggested the problem of determining the possible values of integer circulant determinants. To solve a special case of the problem, Laquer gave a factorization of circulant determinants. In this paper, we give a modest generalization of Laquer's theorem. Also, we give an application of the generalization to integer group determinants.https://ijgt.ui.ac.ir/article_26698_4f2e90fea5379b53ebe60bad2a01ebcc.pdf