The depth of subgroups of Suzuki groups

We determine the combinatorial depth of certain subgroups of simple Suzuki groups Sz(q), among others the depth of their maximal subgroups. We apply these results to determine the ordinary depth of these subgroups.Comment: 15 page

On Oliver's p-group conjecture

Let S be a p-group for an odd prime p. Bob Oliver conjectures that a certain characteristic subgroup X(S) always contains the Thompson subgroup J(S). We obtain a reformulation of the conjecture as a statement about modular representations of p-groups. Using this we verify Oliver's conjecture for groups where S/X(S) has nilpotence class at most two.Comment: 9 pages; terminology altered to conform to current usag

pp-groups with maximal elementary abelian subgroups of rank 22

Let p be an odd prime number and G a finite p-group. We prove that if the rank of G is greater than p, then G has no maximal elementary abelian subgroup of rank 2. It follows that if G has rank greater than p, then the poset of elementary abelian subgroups of G of rank at least 2 is connected and the torsion-free rank of the group of endotrivial kG-modules is one, for any field k of characteristic p. We also verify the class-breadth conjecture for the p-groups G whose poset has more than one component

Halál és halhatatlanság a Phaidónban

Tanulmányomban Platón Phaidónjának egy részletét (105e6–107b10) tárgyalom, melyben Szókratész abból, hogy bebizonyította a lélek halhatatlanságát, arra következtet, hogy a lélek elpusztíthatatlan. Az érvet több szerző is hibásnak tekinti a Platónszakirodalomban – például Taylor, Bostock –, ugyanis abból, hogy valami halhatatlan, nem feltétlenül következik, hogy egyben elpusztíthatatlan is. Ezzel szemben amellett érvelek, hogy a Phaidón korábbi részeiben a halállal és halhatatlansággal kapcsolatban elfogadott premisszák lehetővé teszik, hogy a lélek halhatatlanságából rögtön elpusztíthatatlanságára következtethessünk, aminek fontos előfeltevése, hogy a halált és halhatatlanságot Szókratész itt sokkal szélesebb, metafizikai kontextusban fogja fel, mint ahogy az első pillantásra látszik

Separation and identification of antibacterial chamomile components using OPLC, bioautography and GC-MS

Components of 50% ethanolic chamomile (Matricaria recutica L.) flower extract, previously found antibacterial in a TLC-bioautographic study, were separated and isolated by the use of on-line OPLC, which consisted of an OPLC 50 BS system, an on-line coupled flow-through UV detector, and a manual fraction collector. The collected peaks were investigated by GC-MS analysis and by TLC re-chromatography with subsequent visualization, performed after use of the vanillin-sulphuric acid reagent, or under UV illumination, or applying bioautographic detection. The main compounds of the collected 11 fractions were identified by GC-MS. The results showed that the antibacterial effect of 50% ethanolic extract of chamomile is ascribable to cis-, trans-spiroethers, and the coumarins like herniarin and umbelliferone

On a strong form of Oliver’s p-group conjecture.

We introduce a stronger and more tractable form of Olivers p-group conjecture, and derive a reformulation in terms of the modular representation theory of a quotient group. The Sylow p-subgroups of the symmetric group Sn and of the general linear group satisfy both the strong conjecture and its reformulation