2,450 research outputs found

    QCD measurements in photon-photon collisions at LEP

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    An overview of the latest results of the LEP collaborations on QCD measurements in photon-photon collisions is presented, including measurements of the total hadronic cross-section, the production of heavy quarks and dijets and the structure functions of real and virtual photons.Comment: 6 pages, Talk presented at DPF 2000, Columbus, Ohio, August 200

    Commutators and commutator subgroups in profinite groups

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    Let GG be a profinite group. We prove that the commutator subgroup GG' is finite-by-procyclic if and only if the set of all commutators of GG is contained in a union of countably many procyclic subgroups.Comment: 19 pages, final versio

    Double automorphisms of graded Lie algebras

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    We introduce the concept of a double automorphism of an A-graded Lie algebra L. Roughly, this is an automorphism of L which also induces an automorphism of the group A. It is clear that the set of all double automorphisms of L forms a subgroup in Aut(L). In the present paper we prove several nilpotency criteria for a graded Lie algebra admitting a finite group of double automorphisms. We also give an application of our results to groups admitting a Frobenius group of automorphisms.Comment: 13 page

    On finite groups in which coprime commutators are covered by few cyclic subgroups

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    The coprime commutators γj\gamma_j^* and δj\delta_j^* were recently introduced as a tool to study properties of finite groups that can be expressed in terms of commutators of elements of coprime orders. They are defined as follows. Let GG be a finite group. Every element of GG is both a γ1\gamma_1^*-commutator and a δ0\delta_0^*-commutator. Now let j2j\geq 2 and let XX be the set of all elements of GG that are powers of γj1\gamma_{j-1}^*-commutators. An element gg is a γj\gamma_j^*-commutator if there exist aXa\in X and bGb\in G such that g=[a,b]g=[a,b] and (a,b)=1(|a|,|b|)=1. For j1j\geq 1 let YY be the set of all elements of GG that are powers of δj1\delta_{j-1}^*-commutators. The element gg is a δj\delta_j^*-commutator if there exist a,bYa,b\in Y such that g=[a,b]g=[a,b] and (a,b)=1(|a|,|b|)=1. The subgroups of GG generated by all γj\gamma_j^*-commutators and all δj\delta_j^*-commutators are denoted by γj(G)\gamma_j^*(G) and δj(G)\delta_j^*(G), respectively. For every j2j\geq2 the subgroup γj(G)\gamma_j^*(G) is precisely the last term of the lower central series of GG (which throughout the paper is denoted by γ(G)\gamma_\infty(G)) while for every j1j\geq1 the subgroup δj(G)\delta_j^*(G) is precisely the last term of the lower central series of δj1(G)\delta_{j-1}^*(G), that is, δj(G)=γ(δj1(G))\delta_j^*(G)=\gamma_\infty(\delta_{j-1}^*(G)). In the present paper we prove that if GG possesses mm cyclic subgroups whose union contains all γj\gamma_j^*-commutators of GG, then γj(G)\gamma_j^*(G) contains a subgroup Δ\Delta, of mm-bounded order, which is normal in GG and has the property that γj(G)/Δ\gamma_{j}^{*}(G)/\Delta is cyclic. If j2j\geq2 and GG possesses mm cyclic subgroups whose union contains all δj\delta_j^*-commutators of GG, then the order of δj(G)\delta_j^*(G) is mm-bounded.Comment: Final version, referee's suggestions adde