Maximal Subgroups of Compact Lie Groups

This report aims at giving a general overview on the classification of the maximal subgroups of compact Lie groups (not necessarily connected). In the first part, it is shown that these fall naturally into three types: (1) those of trivial type, which are simply defined as inverse images of maximal subgroups of the corresponding component group under the canonical projection and whose classification constitutes a problem in finite group theory, (2) those of normal type, whose connected one-component is a normal subgroup, and (3) those of normalizer type, which are the normalizers of their own connected one-component. It is also shown how to reduce the classification of maximal subgroups of the last two types to: (2) the classification of the finite maximal Sigma-invariant subgroups of centerfree connected compact simple Lie groups and (3) the classification of the Sigma-primitive subalgebras of compact simple Lie algebras, where Sigma is a subgroup of the corresponding outer automorphism group. In the second part, we explicitly compute the normalizers of the primitive subalgebras of the compact classical Lie algebras (in the corresponding classical groups), thus arriving at the complete classification of all (non-discrete) maximal subgroups of the compact classical Lie groups.

EXTENSION OF AUTOMORPHISMS OF SUBGROUPS

Let G be a group such that, for any subgroup H of G, every automorphism of H can be extended to an automorphism of G. Such a group G is said to be of injective type. The finite abelian groups of injective type are precisely the quasi-injective groups. We prove that a finite non-abelian group G of injective type has even order. If, furthermore, G is also quasi-injective, then we prove that G = K x B, with B a quasi-injective abelian group of odd order and either K = Q(8) (the quaternion group of order 8) or K = Dih(A), a dihedral group on a quasi-injective abelian group A of odd order coprime with the order of B. We give a description of the supersoluble finite groups of injective type whose Sylow 2-subgroup are abelian showing that these groups are, in general, not quasi-injective. In particular, the characterisation of such groups is reduced to that of finite 2-groups that are of injective type. We give several restrictions on the latter. We also show that the alternating group A(5) is of injective type but that the binary icosahedral group SL(2, 5) is not.

Profiling Three-Dimensional Nuclear Telomeric Architecture of Myelodysplastic Syndromes and Acute Myeloid Leukemia Defines Patient Subgroups

Purpose: Myelodysplastic syndromes (MDS) are a group of disorders characterized by cytopenias, with a propensity for evolution into acute myeloid leukemias (AML). This transformation is driven by genomic instability, but mechanisms remain unknown. Telomere dysfunction might generate genomic instability leading to cytopenias and disease progression. Experimental Design: We undertook a pilot study of 94 patients with MDS (56 patients) and AML (38 patients). The MDS cohort consisted of refractory cytopenia with multilineage dysplasia (32 cases), refractory anemia (12 cases), refractory anemia with excess of blasts (RAEB) 1 (8 cases), RAEB2 (1 case), refractory anemia with ring sideroblasts (2 cases), and MDS with isolated del(5q) (1 case). The AML cohort was composed of AML-M4 (12 cases), AML-M2 (10 cases), AML-M5 (5 cases), AML-M0 (5 cases), AML-M1 (2 cases), AML-M4eo (1 case), and AML with multidysplasia-related changes (1 case). Three-dimensional quantitative FISH of telomeres was carried out on nuclei from bone marrow samples and analyzed using TeloView. Results: We defined three-dimensional nuclear telomeric profiles on the basis of telomere numbers, telomeric aggregates, telomere signal intensities, nuclear volumes, and nuclear telomere distribution. Using these parameters, we blindly subdivided the MDS patients into nine subgroups and the AML patients into six subgroups. Each of the parameters showed significant differences between MDS and AML. Combining all parameters revealed significant differences between all subgroups. Three-dimensional telomeric profiles are linked to the evolution of telomere dysfunction, defining a model of progression from MDS to AML. Conclusions: Our results show distinct three-dimensional telomeric profiles specific to patients with MDS and AML that help subgroup patients based on the severity of telomere dysfunction highlighted in the profiles. Clin Cancer Res; 18(12); 3293-304. (C) 2012 AACR.

Locally finite groups with all subgroups either subnormal or nilpotent-by-Chernikov

Let G be a locally finite group satisfying the condition given in the title and suppose that G is not nilpotent-by-Chernikov. It is shown that G has a section S that is not nilpotent-by-Chernikov, where S is either a p-group or a semi-direct product of the additive group A of a locally finite field F by a subgroup K of the multiplicative group of F, where K acts by multiplication on A and generates F as a ring. Non-(nilpotent-by-Chernikov) extensions of this latter kind exist and are described in detail.

GROUPS THAT INVOLVE FINITELY MANY PRIMES AND HAVE ALL SUBGROUPS SUBNORMAL II

It is shown that if G is a hypercentral group with all subgroups subnormal, and if the torsion subgroup of G is a pi-group for some finite set pi of primes, then G is nilpotent. In the case where G is not hypercentral there is a section of G that is much like one of the well-known Heineken-Mohamed groups. It is also shown that if G is a residually nilpotent group with all subgroups subnormal whose torsion subgroup satisfies the above condition then G is nilpotent.

On Groups with Two Isomorphism Classes of Derived Subgroups

The structure of groups which have at most two isomorphism classes of derived subgroups (D-2-groups) is investigated. A complete description of D-2-groups is obtained in the case where the derived subgroup is finite: the solution leads an interesting number theoretic problem. In addition, detailed information is obtained about soluble D-2-groups, especially those with finite rank, where algebraic number fields play an important role. Also, detailed structural information about insoluble D-2-groups is found, and the locally free D-2-groups are characterized.

A spatial-temporal approach to surveillance of prostate cancer disparities in population subgroups

BACKGROUND: Prostate cancer mortality disparities exist among racial/ethnic groups in the United States, yet few studies have explored the spatiotemporal trend of the disease burden. To better understand mortality disparities by geographic regions over time, the present study analyzed the geographic variations of prostate cancer mortality by three Texas racial/ethnic groups over a 22-year period. METHODS: The Spatial Scan Statistic developed by Kulldorff et al was used. Excess mortality was detected using scan windows of 50% and 90% of the study period and a spatial cluster size of 50% of the population at risk. Time trend was analyzed to examine the potential temporal effects of clustering. Spatial queries were used to identify regions with multiple racial/ethnic groups having excess mortality. RESULTS: The most likely area of excess mortality for blacks occurred in Dallas-Metroplex and upper east Texas areas between 1990 and 1999; for Hispanics, in central Texas between 1992 and 1996: and for non-Hispanic whites, in the upper south and west to central Texas areas between 1990 and 1996. Excess mortality persisted among all racial/ethnic groups in the identified counties. The second scan revealed that three counties in west Texas presented an excess mortality for Hispanics from 1980-2001. Many counties bore an excess mortality burden for multiple groups. There is no time trend decline in prostate cancer mortality for blacks and non-Hispanic whites in Texas. CONCLUSION: Disparities in prostate cancer mortality among racial/ethnic groups existed in Texas. Central Texas counties with excess mortality in multiple subgroups warrant further investigation.

Differences in small-for-gestational-age and preterm birth among Asian subgroups in relation to nativity status

This retrospective cohort study examined the association between nativity status and very preterm birth, preterm birth, and small-for-gestational-age (SGA) among Asian subgroups using Texas birth certificate data with no personal identifiers. A total of 877,322 birth certificates of Asian and US-born white women with a singleton birth in Texas from 2001-2004 were analyzed. Birth certificate records of US-born white, Chinese, Japanese, Korean, Vietnamese, Filipino, and Asian Indian women with a singleton birth were included in the analysis. Logistic regressions models were used to explore and understand the differences of the effect of nativity status on birth outcomes in Asian subgroups with US-born whites as the reference group. Most of the Asian subgroups had a lower risk of preterm births compared with US born whites, with reductions in risk ranging from 19% to 49% and the lowest risk of preterm birth observed among foreign-born Chinese mothers. Only Filipino mothers had a higher risk of preterm birth compared to US-born whites. Overall, foreign-born Asians had lower risks for very preterm birth and preterm birth than US-born Asians and US-born whites. US-born Asians were at higher risk for preterm birth than US-born whites. For SGA, all Asian subgroups and Asian subgroups by nativity status were at higher risk of SGA than US-born whites. Asian Indians and Japanese were at highest risk for SGA infants with 2.5 to 3 times the risk of SGA present in US-born whites. Foreign-born Asian women were at higher risk for SGA than their US-born counterparts. This study showed that health disparities among Asian subgroups are hidden by classifying Asians into a single group. By examining Asian subgroups separately and looking at nativity status, the differences in risk of SGA and preterm birth can be revealed so prevention efforts can focus on high risk groups. ^

Late Cenozoic silicoflagellate biostratigraphy, relative paleotemperature, and distribution of various genera and morphologic subgroups with remarks on noteworthy occurrences at DSDP Leg 86 Holes

A quantitative study of late Cenozoic silicoflagellates from the northwestern Pacific sites of Deep Sea Drilling Project Leg 86 shows a relative paleotemperature (Ts) gradient with lowest values (Ts = 30) in the north. Some new ecostratigraphic relations for the region are indicated, such as the last common occurrence of Dictyocha brevispina at 2.6 - 3.0 m.y. ago during a cool interval. Elements of North Pacific and low-latitude biostratigraphic zonations can be identified, but the mixing of cool- and warm-indicator taxa prompted the definition of the new Miocene Mesocena hexalitha Subzone and Pliocene Distephanus jimlingii Subzone. Scanning-electron microscope study of Leg 86 silicoflagellates was done to determine whether various types of skeletal surface texture are temperature dependent. To conduct the study we organized a new surface-texture descriptive code, which characterizes the apical structure/basal ring/spine sequence using new definitions of the terms crenulate (C), linear (L), nodular (N), reticulate (R), and smooth (S). One new silicoflagellate genus, Caryocha Bukry et Monechi, n. gen., is described and several new combinations are made.