University of Isfahan International Journal of Group Theory 2251-7650 7 4 2018 12 01 Locally graded groups with a condition on infinite subsets 1 7 21234 10.22108/ijgt.2016.21234 EN Asadollah Faramarzi Salles Damghan University Fatemeh Pazandeh Shanbehbazari Damghan University Journal Article 2016 02 17 Let \$G\$ be a group‎, ‎we say that \$G\$ satisfies the property \$mathcal{T}(infty)\$ provided that‎, ‎every infinite set of elements of \$G\$ contains elements \$xneq y‎, ‎z\$ such that \$[x‎, ‎y‎, ‎z]=1=[y‎, ‎z‎, ‎x]=[z‎, ‎x‎, ‎y]\$‎.<br /> ‎We denote by \$mathcal{C}\$ the class of all polycyclic groups‎, ‎\$mathcal{S}\$ the class of all soluble groups‎, ‎\$mathcal{R}\$ the class of all residually finite groups‎, ‎\$mathcal{L}\$ the class of all locally graded groups‎, ‎\$mathcal{N}_2\$ the class of all nilpotent group of class at most two‎, ‎and \$mathcal{F}\$ the class of all finite groups‎. ‎In this paper‎, ‎first we shall prove that if \$G\$ is a finitely generated locally graded group‎, ‎then \$G\$ satisfies \$mathcal{T}(infty)\$ if and only if \$G/Z_2(G)\$ is finite‎, ‎and then we shall conclude that if \$G\$ is a finitely generated group in \$mathcal{T}(infty)\$‎, ‎then‎ ‎[Ginmathcal{L}Leftrightarrow Ginmathcal{R}Leftrightarrow Ginmathcal{S}Leftrightarrow Ginmathcal{C}Leftrightarrow Ginmathcal{N}_2mathcal{F}.]‎ https://ijgt.ui.ac.ir/article_21234_67c122bc31064ada379ba0fa8178aec3.pdf
University of Isfahan International Journal of Group Theory 2251-7650 7 4 2018 12 01 Automorphisms of a finite \$p\$-group with cyclic Frattini subgroup 9 16 21219 10.22108/ijgt.2017.21219 EN Rasoul Soleimani Payame Noor University Journal Article 2016 08 08 Let \$G\$ be a group and \$Aut^{Phi}(G)\$ denote the group of all automorphisms of \$G\$ centralizing \$G/Phi(G)\$ elementwise‎. ‎In this paper‎, ‎we characterize the finite \$p\$-groups \$G\$ with cyclic Frattini subgroup for which \$|Aut^{Phi}(G):Inn(G)|=p\$‎. https://ijgt.ui.ac.ir/article_21219_ae7d67b716884474ebab05e35cda245c.pdf
University of Isfahan International Journal of Group Theory 2251-7650 7 4 2018 12 01 On embedding of partially commutative metabelian groups to matrix groups 17 26 21478 10.22108/ijgt.2017.21478 EN E. I. Timoshenko Novosibirsk State Technical University Journal Article 2016 03 06 ‎The Magnus embedding of a free metabelian group induces the embedding of partially commutative metabelian group \$S_Gamma\$ in a group of matrices \$M_Gamma\$. Properties and the universal theory of the group \$M_Gamma\$ are studied. https://ijgt.ui.ac.ir/article_21478_06e8a271d84561be036e425c8e46cc0c.pdf
University of Isfahan International Journal of Group Theory 2251-7650 7 4 2018 12 01 Measuring cones and other thick subsets in free groups 27 40 21479 10.22108/ijgt.2017.21479 EN Elizaveta Frenkel Moscow State University Vladimir Remeslennikov Mathematical Institute SB RAS Journal Article 2016 03 30 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 sets accepted by special automata or special monoids‎. ‎These automata allow us to compute explicitly generating functions‎, ‎\$lambda-\$measures and Cesaro measure of thick monoids‎. ‎Also we improve the asymptotic classification of regular subsets in free groups‎. https://ijgt.ui.ac.ir/article_21479_6002b97cd87509a69bdf9b2e53ab514f.pdf
University of Isfahan International Journal of Group Theory 2251-7650 7 4 2018 12 01 The Maschke property for the Sylow \$p\$-subgroups of the symmetric group \$S_{p^n}\$ 41 64 21610 10.22108/ijgt.2017.21610 EN David J. Green Institut f&uuml;r Mathematik Friedrich-Schiller&uuml;Universit&auml;t 07737 Jena ‎L. Héthelyi Budapest University of Technology and Economics, Mathematical Institute, Department of Algebra H-1111 Budapest, Műegyetem rkp. 3-9. E. Horváth Budapest University of Technology and Economics, Faculty of Sciences, Inst. Math., Department of Algebra, H-1111 Budapest, Műegyetem rkp. 3-9. Journal Article 2016 10 23 ‎‎In this paper we prove that the Maschke property holds for coprime actions on some important classes of \$p\$-groups like‎: ‎metacyclic \$p\$-groups‎, ‎\$p\$-groups of \$p\$-rank two for \$p>3\$ and some weaker property holds in the case of regular \$p\$-groups‎. ‎The main focus will be the case of coprime actions on the iterated wreath product \$P_n\$ of cyclic groups of order \$p\$‎, ‎i.e‎. ‎on Sylow \$p\$-subgroups of the symmetric groups \$S_{p^n}\$‎, ‎where we also prove that a stronger form of the Maschke property holds‎. ‎These results contribute to a future possible classification of all \$p\$-groups with the Maschke property‎. ‎We apply these results to describe which normal partition subgroups of \$P_n\$ have a complement‎. ‎In the end we also describe abelian subgroups of \$P_n\$ of largest size‎. https://ijgt.ui.ac.ir/article_21610_049d5dd2426c246d448583ee0a063476.pdf