The character table of a split extension of the Heisenberg group H1(q)H_1(q) by Sp(2,q)Sp(2,q), qq odd

In this paper we determine the full character table of a certain split extension $H_1(q)\rtimes Sp(2,q)$ of the Heisenberg group $H_1$ by the odd-characteristic symplectic group $Sp(2,q)$.Comment: 9 page

The structure of blocks with a Klein four defect group

We prove Erdmann’s conjecture [16] stating that every block with a Klein four defect group has a simple module with trivial source, and deduce from this that Puig’s finiteness conjecture holds for source algebras of blocks with a Klein four defect group. The proof uses the classification of finite simple groups

Mechanism of formation water molecules and chemical bonds in Leptothrix materials

The provided study involves investigating chemical interactions in Leptothrix biomaterial through infrared spectroscopy. The analysis explores variations in chemical relationships based on the nature of chemical bonds and biomaterial coordinates. The primary chemical bonds identified in the biomaterial are associated with Fe-O vibrations and resonances of [OH] functional groups. Additionally, the study presents model representations detailing the formation mechanism of water molecules within the Leptothrix matrix. Model calculations for a two-vacancy cluster defect structure in Fe2O3 and Fe3O4 reveal lifetimes of 180 ps and 174 ps, respectively.http://jomardpublishing.com/journals.aspx?lang=en&id=13hj2024PhysicsNon

Character restrictions and multiplicities in symmetric groups

We give natural correspondences of odd-degree characters of the symmetric groups and some of their subgroups, which can be described easily by restriction of characters, degrees and multiplicities.Prometeo II/Generalitat Valenciana, Proyectos [MTM2016-76196-P]; NSF [DMS-1201374]24 month embargo; Available online 27 January 2017This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]