pp-Groups for which each outer pp-automorphism centralizes only pp elements

An automorphism of a group is called outer if it is not an inner automorphism. Let $G$ be a finite $p$-group. Then for every outer $p$-automorphism $\phi$ of $G$ the subgroup $C_G(\phi)=\{x\in G \;|\; x^\phi=x\}$ has order $p$ if and only if $G$ is of order at most $p^2$

Groups of Order 2048 with Three Generators and Three Relations

It is shown that there are exactly seventy-eight 3-generator 2- groups of order 2^11 with trivial Schur multiplier. We then give 3-generator, 3-relation presentations for forty-eight of them proving that these groups have deficiency zero

Tunnel Magnetoresistance of a Single-Molecule Junction

Based on the non-equilibrium Green's function (NEGF) technique and the Landauer-B\"{u}ttiker theory, the possibility of a molecular spin-electronic device, which consists of a single C$_{60}$ molecule attached to two ferromagnetic electrodes with finite cross sections, is investigated. By studying the coherent spin-dependent transport through the energy levels of the molecule, it is shown that the tunnel magnetoresistance (TMR) of the molecular junction depends on the applied voltages and the number of contact points between the device electrodes and the molecule. The TMR values more than 60% are obtained by adjusting the related parameters.Comment: 5 pages, 3 figure