2019-05-24T22:50:19Z http://ijgt.ui.ac.ir/?_action=export&rf=summon&issue=4127
2018-12-01 10.22108
International Journal of Group Theory Int. J. Group Theory 2251-7650 2251-7650 2018 7 4 Locally graded groups with a condition on infinite subsets Asadollah Faramarzi Salles Fatemeh Pazandeh Shanbehbazari 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}.]‎ ‎Finitely generated groups‎ ‎Residually finite groups‎ ‎Locally graded groups 2018 12 01 1 7 http://ijgt.ui.ac.ir/article_21234_67c122bc31064ada379ba0fa8178aec3.pdf
2018-12-01 10.22108
International Journal of Group Theory Int. J. Group Theory 2251-7650 2251-7650 2018 7 4 Automorphisms of a finite \$p\$-group with cyclic Frattini subgroup Rasoul Soleimani 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\$‎. ‎‎Automorphism group‎ ‎Finite \$p\$-group‎ ‎Frattini subgroup‎ 2018 12 01 9 16 http://ijgt.ui.ac.ir/article_21219_ae7d67b716884474ebab05e35cda245c.pdf
2018-12-01 10.22108
International Journal of Group Theory Int. J. Group Theory 2251-7650 2251-7650 2018 7 4 On embedding of partially commutative metabelian groups to matrix groups E. I. Timoshenko ‎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. Partially commutative group Metabeliah group universal theory Equations in group 2018 12 01 17 26 http://ijgt.ui.ac.ir/article_21478_06e8a271d84561be036e425c8e46cc0c.pdf
2018-12-01 10.22108
International Journal of Group Theory Int. J. Group Theory 2251-7650 2251-7650 2018 7 4 Measuring cones and other thick subsets in free groups Elizaveta Frenkel Vladimir Remeslennikov 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. free group ‎\$lambda-\$measure regular subset special automaton thick monoid 2018 12 01 27 40 http://ijgt.ui.ac.ir/article_21479_6002b97cd87509a69bdf9b2e53ab514f.pdf
2018-12-01 10.22108
International Journal of Group Theory Int. J. Group Theory 2251-7650 2251-7650 2018 7 4 The Maschke property for the Sylow \$p\$-sub-groups of the symmetric group \$S_{p^n}\$ David Green ‎L. H'ethelyi E. Horv'ath ‎‎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. ‎Maschke's Theorem‎ ‎coprime action‎ ‎Sylow \$p\$-subgroup of symmetric group‎ ‎iterated wreath product‎ ‎uniserial action 2018 12 01 41 64 http://ijgt.ui.ac.ir/article_21610_049d5dd2426c246d448583ee0a063476.pdf