Green Correspondence for Virtually Pro-p Groups

Let p be prime, k a finite field of characteristic p, and G a virtually pro-p group. We prove an analogue of the Green Correspondence for finitely generated modules over the completed group algebra k[[G]].Comment: 7 pages. Based on material from author's PhD at Manchester Universit

Modular Representations of Profinite Groups

Our aim is to transfer several foundational results from the modular representation theory of finite groups to the wider context of profinite groups. We are thus interested in profinite modules over the completed group algebra k[[G]] of a profinite group G, where k is a finite field of characteristic p. We define the concept of relative projectivity for a profinite k[[G]]-module. We prove a characterization of finitely generated relatively projective modules analogous to the finite case with additions of interest to the profinite theory. We introduce vertices and sources for indecomposable finitely generated k[[G]]-modules and show that the expected conjugacy properties hold - for sources this requires additional assumptions. Finally we prove a direct analogue of Green's Indecomposability Theorem for finitely generated modules over a virtually pro-p group.Comment: 19 page

Brauer Theory for Profinite Groups

Brauer Theory for a finite group can be viewed as a method for comparing the representations of the group in characteristic 0 with those in prime characteristic. Here we generalize much of the machinery of Brauer theory to the setting of profinite groups. By regarding Grothendieck groups as functors we describe corresponding Grothendieck groups for profinite groups, and generalize the decomposition map, regarded as a natural transformation. We discuss characters and Brauer characters for profinite groups. We give a functorial description of the block theory of a profinite group. We finish with a method for computing the Cartan matrix of a finite group $G$ given the Cartan matrix for a quotient of $G$ by a normal $p$-subgroup.Comment: 16 page

Parachute Engineers in Combat, Ortona 1943: A German Perspective

In late 1943, Allied forces were fighting their way up the Italian peninsula. It was tough going. Broken terrain hindered the advance and well-armed, well-led German defenders fought for nearly every river corssing, hill, and village. On 6 December, Canadian troops, operating on the far right of the Allied line, began to cross the Moro River on the Adriatic coast, battling north through a series of small towns, farms, and ravines. First Canadian Infantry Division under Major-General Chris Vokes, pushing up the coastal highway, met bitter resistance at “The Gully,” a natural feature just north of the Moro. After being driven from this objective, German troops of the 76th Panzer Corps, including two elite parachute battalions, prepared to defend the ancient coastal town of Ortona, whose stout buildings provided scores of excellent defensive positions. The Canadians attacked nevertheless and spent the Christmas season in a bloody house-to-house struggle against determined opposition. By 27 December, with German troops retreating northward, the Canadians had prevailed, though at heavy cost. The Loyal Edmonton Regiment suffered 172 casualties at Ortona, the Seaforth Highlanders 103. Other units’ losses in and around the town, including those of the 12th Armoured Regiment Three Rivers Regiment, brought total Canadian casualties during the battle to 350. While there are numerous Canadian accounts of the battle of Ortona, there are few accounts in English of the fighting from the German perspective. Recently the Canadian War Museum acquired a copy of the following memoir through the good offices of Alex MacQuarrie of HSN Linguistic Services, Ottawa. The narrative, translated by Mr. MacQuarrie, is written by Parachute Combat Engineer Carl Bayerlein (Service No. L25475), 3rd Platoon, 3rd Company, 1st Parachute Combat Engineer Battalion, 1 Parachute Infantry Division. It covers the period of 10–27 December 1943 and consists of two parts: a day-by-day diary account, and a somewhat longer summary, based on the diary entries, but compiled in the early 1990s. The edited version that follows is drawn from the summary account

Parental attributions regarding sleep problems of children with an autism spectrum disorder or Down syndrome, and clinical research portfolio

This study aimed to investigate any difference between the attributions parents made about their child’s sleep problem, in parents of children with an Autism Spectrum Disorder and parents of children with Down Syndrome. Seventy-six parents of children with an Autism Spectrum Disorder and fifty-two parents of children with Down Syndrome completed a series of questionnaires on-line, regarding their child’s sleep problem, their beliefs about their child’s sleep problem and the parent’s level of anxiety and depression. A significant difference was found between the groups on four of the causal items; other health problem, child’s emotional state, child’s personality and diet. Parents of children with Down Syndrome showed a higher level of agreement that their child’s sleep problem could be attributed to another health problem compared to parents of children with an Autism Spectrum Disorder. Parents of children with an Autism Spectrum Disorder showed a higher level of agreement that their child’s sleep problem could be attributed to their child’s personality, their child’s emotional state and their child’s diet compared to parents of children with DS. There was a high level of agreement across all parents that their child’s disability was a causal factor to their sleep problem and differences in attributions may reflect characteristics of the child’s diagnosis. The results are consistent with previous findings that parents view disability as an important causal factor to their child’s sleep problem and suggest a possible overlap in parent’s views of their child’s sleep problem and views of their disability

Growing up in Nature: Health and Adolescent Dance in L.M. Montgomery’s Emily Series

As the 1890s closed, a new vision of dance was being formed in North America; modern dance, as envisioned by iconic dancer Isadora Duncan, would create a nation of healthy, strong bodies. The same vision of a creative, empowering nature, articulated through the contemporary language of dance and movement, permeates L.M. Montgomery’s Emily series. Ideas about the freedom of dance and the inspirational power of nature, as outlined by Duncan and by Francis Delsarte, are integral to the construction of adolescent health in Montgomery’s texts. Like Duncan and Delsarte, Emily Starr understands the link between her interior soul and external nature, and seems unable to resist expressing that connection through movement. Furthermore, Emily displays what Duncan describes as the natural desire for freedom of all living things. She proves that dancing can be beneficial mentally, physically, and morally, and shows that movement – particularly in nature – can free the adolescent soul

Breakfast is the Most Important Meal of the Day: An Investigation of the Levels of Cadmium in Breakfast Cereal

Cadmium (Cd) is a transition metal that offers no nutritional value to human beings. Humans’ main exposure to Cd is through consumption. Cd is extremely soluble, leading to plants readily absorbing it through contaminated water. Plants containing the absorbed Cd are consumed, and the metal accumulates in the body and is toxic. Effects of Cd in the body include renal tubular damage, pulmonary emphysema, epigenetic changes, and carcinogenesis. Previous studies have looked at Cd in cereal based products, and their results revealed low, varied amounts of Cd in the samples. However, most of these studies were performed in Asian countries. This leaves a gap in data for foods in the United States. This study looks at three different rice cereal brands from grocery stores in the Worcester, MA area. In a 2 g sample, the results ranged from 0.04 ± 0.03 μg in Rice Chex (General Mills), 0.06 ± 0.04 μg in Signature Select’s Rice Pockets (Shaws), and 0.09 ± 0.06 μg in Food Club’s Rice Squares (Big Y). These results were all above the LOD of 0.015 μg. The amounts of Cd found were comparable with the amounts found in previous literature. Since the levels of Cd were below the TWI of 2.5 μg/kg body weight, it can be concluded that the amount of Cd in these brands do not pose a health risk