Subgroup-Specific Diagnostic, Prognostic, and Predictive Markers Influencing Pediatric Medulloblastoma Treatment

Medulloblastoma (MB) is the most common malignant central nervous system tumor in pediatric patients. Mainstay of therapy remains surgical resection followed by craniospinal radiation and chemotherapy, although limitations to this therapy are applied in the youngest patients. Clinically, tumors are divided into average and high-risk status on the basis of age, metastasis at diagnosis, and extent of surgical resection. However, technological advances in high-throughput screening have facilitated the analysis of large transcriptomic datasets that have been used to generate the current classification system, dividing patients into four primary subgroups, i.e., WNT (wingless), SHH (sonic hedgehog), and the non-SHH/WNT subgroups 3 and 4. Each subgroup can further be subdivided on the basis of a combination of cytogenetic and epigenetic events, some in distinct signaling pathways, that activate specific phenotypes impacting patient prognosis. Here, we delve deeper into the genetic basis for each subgroup by reviewing the extent of cytogenetic events in key genes that trigger neoplastic transformation or that exhibit oncogenic properties. Each of these discussions is further centered on how these genetic aberrations can be exploited to generate novel targeted therapeutics for each subgroup along with a discussion on challenges that are currently faced in generating said therapies. Our future hope is that through better understanding of subgroup-specific cytogenetic events, the field may improve diagnosis, prognosis, and treatment to improve overall quality of life for these patients.

Finite groups with σ-Frobenius condition for non-normal σ-primary subgroups

Let [Formula: see text] be a partition of the set [Formula: see text] of all primes and [Formula: see text] a finite group. A group is said to be [Formula: see text]-primary if it is a finite [Formula: see text]-group for some [Formula: see text]. We say that a [Formula: see text]-subgroup [Formula: see text] of [Formula: see text] satisfies the [Formula: see text]-Frobenius condition in [Formula: see text] if [Formula: see text] is a [Formula: see text]-group. In this paper, we determine the structure of finite groups in which every non-normal [Formula: see text]-primary subgroup satisfies the [Formula: see text]-Frobenius condition.