2019-05-24T23:18:29Z http://ijgt.ui.ac.ir/?_action=export&rf=summon&issue=4093
2018-06-01 10.22108
International Journal of Group Theory Int. J. Group Theory 2251-7650 2251-7650 2018 7 2 Sylow multiplicities in finite groups Dan Levy Let \$G\$ be a finite group and let \$mathcal{P}=P_{1},ldots,P_{m}\$ be a sequence‎ ‎of Sylow \$p_{i}\$-subgroups of \$G\$‎, ‎where \$p_{1},ldots,p_{m}\$ are the distinct‎ ‎prime divisors of \$leftvert Grightvert \$‎. ‎The Sylow multiplicity of \$gin‎ ‎G\$ in \$mathcal{P}\$ is the number of distinct factorizations \$g=g_{1}cdots‎ ‎g_{m}\$ such that \$g_{i}in P_{i}\$‎. ‎We review properties of the solvable‎ ‎radical and the solvable residual of \$G\$ which are formulated in terms of‎ ‎Sylow multiplicities‎, ‎and discuss some related open questions‎. ‎Sylow sequences‎ ‎Sylow multiplicities‎ ‎Solvable radical‎ ‎Solvable residual 2018 06 01 1 8 http://ijgt.ui.ac.ir/article_21482_4d16a7d4c6f2488422da19da3ac6bcf6.pdf
2018-06-01 10.22108
International Journal of Group Theory Int. J. Group Theory 2251-7650 2251-7650 2018 7 2 Some characterisations of groups in which normality is a‎ ‎transitive relation by means of subgroup embedding properties Ramon Esteban-Romero Giovanni Vincenzi ‎In this survey we highlight the relations between some subgroup embedding properties that characterise groups in which normality is a transitive relation in‎ ‎certain universes of groups with some finiteness properties‎. ‎group‎ ‎subgroup‎ ‎embedding property‎ ‎T-group‎ ‎FC\$^*\$-group‎ ‎group without infinite‎ ‎simple sections 2018 06 01 9 16 http://ijgt.ui.ac.ir/article_21214_cc340e8f12a5cd3c8681717909e787b8.pdf
2018-06-01 10.22108
International Journal of Group Theory Int. J. Group Theory 2251-7650 2251-7650 2018 7 2 On finite groups with square-free conjugacy class sizes Maria-Jose Felipe Ana Martinez-Pastor Victor-Manuel Ortiz-Sotomayor We report on fi nite groups having square-free conjugacy class sizes, in particular in the framework of factorised groups. Finite groups Conjugacy classes Factorised groups 2018 06 01 17 24 http://ijgt.ui.ac.ir/article_21475_3c37cb4c86113971ca7d07fb160d560a.pdf
2018-06-01 10.22108
International Journal of Group Theory Int. J. Group Theory 2251-7650 2251-7650 2018 7 2 On metacyclic subgroups of finite groups Adolfo Ballester-Bolinches ‎The aim of this survey article is to present some structural results about of groups whose Sylow <em>p</em>-subgroups are metacylic (<em>p</em> a prime)‎. ‎A complete characterisation of non-nilpotent groups whose <em>2</em>-generator subgroups are metacyclic is also presented‎. Finite group Sylow subgroups metacyclic groups 2-generator groups 2018 06 01 25 29 http://ijgt.ui.ac.ir/article_21480_b9d4162cb9b5fc9711b0f39d833cf4e0.pdf
2018-06-01 10.22108
International Journal of Group Theory Int. J. Group Theory 2251-7650 2251-7650 2018 7 2 Representations of group rings and groups Ted Hurley An isomorphism between the group ring of a finite group and a ring of certain block diagonal matrices is established. It is shown that for any group ring matrix \$A\$ of \$mathbb{C} G\$ there exists a matrix \$U\$ (independent of \$A\$) such that \$U^{-1}AU= diag(T_1,T_2,ldots, T_r)\$ for block matrices \$T_i\$ of fixed size \$s_i × s_i\$ where \$r\$ is the number of conjugacy classes of \$G\$ and \$s_i\$ are the ranks of the group ring matrices of the primitive idempotents. <br /> <br /> Using the isomorphism of the group ring to the ring of group ring matrices followed by the mapping \$Amapsto P^{-1}AP\$ (fixed \$P\$) gives an isomorphism from the group ring to the ring of such block matrices. Specialising to the group elements gives a faithful representation of the group. Other representations of \$G\$ may be derived using the blocks in the images of the group elements. <br /> <br /> For a finite abelian group \$Q\$ an explicit matrix \$P\$ is given which diagonalises any group ring matrix of \$mathbb{C}Q\$. The characters of \$Q\$ and the character table of \$Q\$ may be read off directly from the rows of the diagonalising matrix \$P\$. This is a special case of the general block diagonalisation process but is arrived at independently. The case for cyclic groups is well-known: Circulant matrices are the group ring matrices of the cyclic group and the Fourier matrix diagonalises any circulant matrix. This has applications to signal processing. group ring Representation 2018 06 01 31 44 http://ijgt.ui.ac.ir/article_21484_2d64c759c091beeacf98923cde8ed7f6.pdf
2018-06-01 10.22108
International Journal of Group Theory Int. J. Group Theory 2251-7650 2251-7650 2018 7 2 On the dimension of the product \$[L_2,L_2,L_1]\$‎ in free Lie algebras Nil Mansuroğlu Let \$L\$ be a free Lie algebra of rank \$rgeq2\$ over a field \$F\$ and let \$L_n\$ denote the degree \$n\$ homogeneous component of \$L\$‎. ‎By using the dimensions of the corresponding homogeneous and fine homogeneous components of the second derived ideal of free centre-by-metabelian Lie algebra over a field \$F\$‎, ‎we determine the dimension of \$[L_2,L_2,L_1]\$‎. ‎Moreover‎, ‎by this method‎, ‎we show that the dimension of \$[L_2,L_2,L_1]\$ over a field of characteristic \$2\$ is different from the dimension over a field of characteristic other than \$2\$.<br /><br /> Free Lie algebra homogeneous and fine homogeneous components free centre-by-metabelian Lie algebra second derived ideal 2018 06 01 45 50 http://ijgt.ui.ac.ir/article_21481_0b392ad1ffab7cd79272442ecc91712c.pdf