University of IsfahanInternational Journal of Group Theory2251-765010120210301Recognition of Janko groups and some simple $K_4$-groups by the order and one irreducible character degree or character degree graph1102371910.22108/ijgt.2019.113029.1502ENHoshangBehraveshDepartment of Mathematics, Urmia University, Urmia , IranMehdiGhaffarzadehDepartment of Mathematics, Khoy Branch, Islamic Azad University, Khoy , IranMohsenGhasemiDepartment of Mathematics, Urmia University, Urmia , IranSomayehHekmataraDepartment of Mathematics, Urmia University, Urmia , IranJournal Article20180923In this paper we prove that some Janko groups are uniquely determined by their orders and one irreducible character degree. Also we prove that some finite simple $K_4$-groups are uniquely determined by their character degree graphs and their orders.https://ijgt.ui.ac.ir/article_23719_bd990adbcf2b607f38e9948294016161.pdfUniversity of IsfahanInternational Journal of Group Theory2251-765010120210301The character table of a sharply $5$-transitive subgroup of the alternating group of degree 1211302352410.22108/ijgt.2019.115366.1531ENNickGillDepartment of Mathematics, University of South Wales, Treforest, CF37 1DL, U. K.SamHughesDepartment of Mathematics, University of South Wales, Treforest, CF37 1DL, U. K.0000-0002-9992-4443Journal Article20190129We calculate the character table of a sharply $5$-transitive subgroup of Alt(12), and of a sharply $4$-transitive subgroup of Alt(11). Our presentation of these calculations is new because we make no reference to the sporadic simple Mathieu groups, and instead deduce the desired character tables using only the existence of the stated multiply transitive permutation representations.https://ijgt.ui.ac.ir/article_23524_7f2711ca3af41b2aeed2654b5571c9ce.pdfUniversity of IsfahanInternational Journal of Group Theory2251-765010120210301Weakly totally permutable products and Fitting classes31382352510.22108/ijgt.2019.115685.1535ENSesuai YashMadanhaDepartment of Mathematics and Applied Mathematics, University of Pretoria, Private bag X20, Hatfield, 0028, Pretoria,
South AfricaJournal Article20190224It is known that if $ G=AB $ is a product of its totally permutable subgroups $ A $ and $ B $, then $ G\in \mathfrak{F} $ if and only if $ A\in \mathfrak{F} $ and $ B\in \mathfrak{F} $ when $ \mathfrak{F} $ is a Fischer class containing the class $ \mathfrak{U} $ of supersoluble groups. We show that this holds when $ G=AB $ is a weakly totally permutable product for a particular Fischer class, $ \mathfrak{F}\diamond \mathfrak{N} $, where $ \mathfrak{F} $ is a Fitting class containing the class $ \mathfrak{U} $ and $ \mathfrak{N} $ a class of nilpotent groups. We also extend some results concerning the $ \mathfrak{U} $-hypercentre of a totally permutable product to a weakly totally permutable product.https://ijgt.ui.ac.ir/article_23525_2c627dd163f8690b758fb2c0651fc819.pdfUniversity of IsfahanInternational Journal of Group Theory2251-765010120210301A note on locally soluble almost subnormal subgroups in divsion rings39462381310.22108/ijgt.2019.116399.1546ENTruongHuu DungFaculty of Mathematics and Computer Science, VNUHCM-University of Science, 227 Nguyen Van Cu Str., Dist. 5,
HCM-City, VietnamJournal Article20190411Let $D$ be a division ring with center $F$ and assume that $N$ is a locally soluble almost subnormal subgroup of the multiplicative group $D^*$ of $D$. We prove that if $N$ is algebraic over $F$, then $N$ is central. This answers partially \cite[Conjecture 1]{hai_13}.https://ijgt.ui.ac.ir/article_23813_7fdc0ec932613c6a2824e6a33c1a11a8.pdfUniversity of IsfahanInternational Journal of Group Theory2251-765010120210301Characterization of finite groups with a unique non-nilpotent proper subgroup47532385910.22108/ijgt.2019.116209.1543ENBijanTaeriDepartment of Mathematical Sciences, Isfahan University of Technology, P.O.Box 84156-83111, Isfahan, IranFatemehTayanloo-BeygDepartment of Mathematical Sciences, Isfahan University of Technology, P.O.Box 84156-83111, Isfahan, IranJournal Article20190326We characterize finite non-nilpotent groups $G$ with a unique non-nilpotent proper subgroup. We show that $|G|$ has at most three prime divisors. When $G$ is supersolvable we find the presentation of $G$ and when $G$ is non-supersolvable we show that either $G$ is a direct product of an Schmidt group and a cyclic group or a semi direct product of a $p$-group by a cyclic group of prime power order.https://ijgt.ui.ac.ir/article_23859_ef34d72855971a0ebedf02706bdfb1e2.pdf