Solution. The 11-Sylow subgroup is Z/11Z; the 5-Sylow subgroup is Z/5Z. By Sylow’s theorem, the 11-Sylow subgroup is normal. Hence, the group is a semi-direct product of its 5 and 11-Sylow subgroups. Since Aut(Z/11Z) = Z/10Z has a unique subgroup of order 5, there are up to isomorphism exactly two groups of order 55: the abelian group Z/55Z and the group with presentation ⟨x, y|x = y = 1, xyx−1...

Solution: For the action mentioned in the hint, the stabilizer of the coset eH (e is the identity) is H since gH = H implies that g ∈ H. The kernel K of the homomorphism of G into the permutation group of the cosets is a normal subgroup of G which is the intersection of stabilizers of all cosets. In particular the kernel K of the above homomorphism is a subgroup of H. Its index in G is equal to...

Let G have order 2013. For p = 3, 11, 61 denote by np the number of Sylow p-groups in G. By Sylow’s theorems we have 61 | (n61 − 1) and n61|33, which is possible only for n61 = 1. Hence the 61-Sylow subgroup B is unique and therefore normal in G. Similarly, n11 | 3× 61 and 11 | (n11 − 1) yields n11 = 1; and the unique 11-Sylow subgroup A is normal in G. Note that A ∩ B is the trivial subgroup {...

recurring after a short time, was successfully treated by radium. It is interesting to note in the present series (Cases 3 anid 4), the dlifference in response to radium of two growths which histologically are very similar. Generally it would seem if the situation of the growth is such that it (loes not reaclily permit of removal of a wedge of normal tissue together with the tumour, surgical in...

So, at altitudes above 1,000 m, the dragonfl ies could be able to reach the Maldives using these winds. Studies in China have found the dragonfl ies fl ying at these heights and studies of air pollutants have shown that they can spread from southern India to the Maldives at speeds of 10 m per second. With such tailwinds, dragonfl ies might make the crossing from India to Male in 24 hours or les...

The development of an experimental environment with interactive features, suitable both for the reinforcement of undergraduate level teaching of control theory and also for graduate-level research work in the field of intelligent control is described. The students are prepared for the experiment by an interactive session on the Internet before coming into the laboratory. The hardware and the so...

The high-pressure lattice dynamics and superconductivity of newly proposed lithium hydrides (LiH2, LiH6 and LiH8) have been extensively studied using density functional theory. The application of the Allen-Dynes modified McMillan equation and electron-phonon coupling calculations show that LiH6 and LiH8 are superconductors with critical temperatures (T(c)) of 38 K at 150 GPa for LiH6 and 31 K a...

M. Bedny, A. Caramazza, A. Pascual-Leone and R. Saxe Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, USA, Berenson-Allen Center for Noninvasive Brain Stimulation, Beth Israel Deaconess Medical Center, Harvard Medical School, Boston, MA 02215, USA, Department of Psychology, Harvard University, William James Hall, Cambridge, MA 02138, USA an...

In this note, we consider a nonlinear diffusion equation with a bistable reaction term arising in population dynamics. Given a rather general initial data, we investigate its behavior for small times as the reaction coefficient tends to infinity: we prove a generation of interface property.