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 $p^2$

How to Compute Modulo Prime-Power Sums

The problem of computing modulo prime-power sums is investigated in distributed source coding as well as computation over Multiple-Access Channel (MAC). We build upon group codes and present a new class of codes called Quasi Group Codes (QGC). A QGC is a subset of a group code. These codes are not closed under the group addition. We investigate some properties of QGC's, and provide a packing and a covering bound. Next, we use these bounds to derived achievable rates for distributed source coding as well as computation over MAC. We show that strict improvements over the previously known schemes can be obtained using QGC's

Investigating dimensional and geometrical accuracy of isothermally forged blades

Compressor blades are one of the well-known products made of titanium alloys. They are usually manufactured by a forging process followed by a sequence of machining processes. Precision forging eliminates a considerable amount of machining; however, due to the close tolerances, the process should be designed in a manner to meet dimensional and geometrical tolerances as well as the desired mechanical and metallurgical properties. In this paper, effects of two main process parameters, the process temperature and strain rate, on the dimensional and geometrical accuracy of the isothermally forged blades are investigated experimentally. The results are analyzed by the response surface method (RSM). In order to justify the results and have a tool for further studies, a coupled thermo-mechanical finite element method model is developed and verified by the experimental results. The results show that the process temperature and pressing speed and their interaction have a meaningful effect on the thickness error; however, the interaction effect of the process temperature and pressing speed on the twist error is not considerable and moreover the bow error of the forged blades is not significant. Finally, the results show that for a given geometry, by selection of appropriate process parameters, a sound workpiece with acceptable dimensional and geometrical aspects can be manufactured without any need for a die shape compensation