"On the Taketa bound for normally monomial p-groups of maximal class"

Geoffrey T. Tims is a 2003 graduate of the Department of Mathematics and Computer Science, Drake University.A longstanding problem in the representation theory of finite solvable groups, sometimes called the Taketa problem, is to find strong bounds for the derived length dl(G) in terms of the number |cd(G)| of irreducible character degrees of the group G. For p-groups an old result of Taketa implies that dl(G)|cd(G)|, and while it is conjectured that the true bound is much smaller (in fact, logarithmic) for large dl(G), it turns out to be extremely difficult to improve on Taketa's bound at all. Here, therefore, we suggest to first study the problem for a restricted class of p-groups, namely normally monomial p-groups of maximal class. We exhibit some structural features of these groups and show that if G is such a group, then .Supported by NSF REU grant #0097759

Late Pleistocene glaciation of the Mt Giluwe volcano, Papua New Guinea

The Mt Giluwe shield volcano was the largest area glaciated in Papua New Guinea during the Pleistocene. Despite minimal cooling of the sea surface during the last glacial maximum, glaciers reached elevations as low as 3200 m. To investigate changes in the extent of ice through time we have re-mapped evidence for glaciation on the southwest flank of Mt Giluwe. We find that an ice cap has formed on the flanks of the mountain on at least three, and probably four, separate occasions. To constrain the ages of these glaciations we present 39 new cosmogenic 36Cl exposure ages complemented by new radiocarbon dates. Direct dating of the moraines identifies that the maximum extent of glaciation on the mountain was not during the last glacial maximum as previously thought. In conjunction with existing potassium/argon and radiocarbon dating, we recognise four distinct glacial periods between 293-306 ka (Gogon Glaciation), 136-158 ka (Mengane Glaciation), centred at 62 ka (Komia Glaciation) and from >20.3-11.5 ka (Tongo Glaciation). The temperature difference relative to the present during the Tongo Glaciation is likely to be of the order of at least 5 °C which is a minimum difference for the previous glaciations. During the Tongo Glaciation, ice was briefly at its maximum for less than 1000 years, but stayed near maximum levels for nearly 4000 years, until about 15.4 ka. Over the next 4000 years there was more rapid retreat with ice free conditions by the early Holocene