In mathematics, specifically group theory, an abnormal subgroup is a subgroup H of a group G such that for all x in G, x lies in the subgroup generated by H and Hx, where Hx denotes the conjugate subgroup xHx−1.
Here are some facts relating abnormality to other subgroup properties:
Every abnormal subgroup is a self-normalizing subgroup, as well as a contranormal subgroup.
The only normal subgroup that is also abnormal is the whole group.
Every abnormal subgroup is a weakly abnormal subgroup, and every weakly abnormal subgroup is a self-normalizing subgroup.
Every abnormal subgroup is a pronormal subgroup, and hence a weakly pronormal subgroup, a paranormal subgroup, and a polynormal subgroup.
specifically group theory, an abnormalsubgroup is a subgroup H of a group G such that for all x in G, x lies in the subgroup generated by H and H x, where...
subgroup of a descendant subgroup. Every abnormalsubgroup is contranormal. Rose 1968, p. 97 Rose, John S. (1968), "Nilpotent Subgroups of Finite Soluble Groups"...
subgroup is a subgroup that is embedded in a nice way. Pronormality is a simultaneous generalization of both normal subgroups and abnormalsubgroups such...
subgroup properties: Every pronormal subgroup, and hence, every normal subgroup and every abnormalsubgroup, is paranormal. Every paranormal subgroup...
descendants of the Fugates were born with met-H. The disorder can cause heart abnormalities and seizures if the amount of methemoglobin in the blood exceeds 20...
into distinct subgroups based on the clinical features and serological status, e.g. affected muscle group, age of onset, thymic abnormalities, and profile...
hepatomegaly Abnormal granules in cells, abnormal nuclear shape and size Chromosome abnormality, including chromosomal translocations and abnormal chromosome...
of the uterus or womb) or, more rarely, anus (in both men and women). Abnormal findings are often followed up by more sensitive diagnostic procedures...
abnormal uterine bleeding (AUB) in the reproductive years. This page is a summary of the systems and their use in contemporary gynecology. Abnormal uterine...
diseases such as asthma. Specifically, this work has demonstrated that a subgroup of severe asthma patients has airway inflammation that is resistant to...
in the muscle becoming an abnormal size, such as muscle atrophy (abnormally small) or a pseudoathletic appearance (abnormally large). Capture myopathy...
categorized into four subgroups, A, B, C and T. An infected cat has a combination of FeLV-A and one or more of the other subgroups. Symptoms, prognosis...
with the syndrome but have some hematological cells containing genetic abnormalities that are similar to those found in Down syndrome. TMD usually develops...
Microangiopathic hemolytic anemia (MAHA) is a microangiopathic subgroup of hemolytic anemia (loss of red blood cells through destruction) caused by factors...
studies have suggested that the main factor which explains the metabolic abnormalities in MONW individuals is fat distribution. On the basis of these studies...
such as seen with non-celiac gluten sensitivity or abnormalities in the gut microbiota. A subgroup of persons with schizophrenia present an immune response...
defined as "disorders characterized by morphologically and functionally abnormal myocardium in the absence of any other disease that is sufficient, by itself...
gentle touch which would not otherwise cause pain or to painful stimuli. Abnormal sensations and itching may also occur. Postherpetic neuralgia is the most...
PSC is unknown. Genetic susceptibility, immune system dysfunction, and abnormal composition of the gut flora may play a role. This is further suggested...
recognition as a separate "national" group, but are rather classified as a subgroup of Bulang. The endonym "Khmu" is suspected to stem from their word kymhmuʔ...
developing bipolar disorder. Neuroimaging and postmortem studies have found abnormalities in a variety of brain regions, and most commonly implicated regions...
The most common type is known as sickle cell anemia. It results in an abnormality in the oxygen-carrying protein haemoglobin found in red blood cells....
stupor, drowsiness, or coma. Babinki’s sign, facial weakness, pupil abnormalities, bulbar palsy, and nystagmus are also commonly found. Symptoms tend...
immunodeficiency virus (HIV) infects and destroys T cells (specifically, the CD4+ subgroup of T lymphocytes, which become helper T cells). Without the key defense...
often[quantify] takes place under ultrasound guidance after venous abnormalities have been diagnosed with duplex ultrasound. Sclerotherapy under ultrasound...
myelodysplastic syndromes and myeloproliferative diseases are myeloid in origin. A subgroup of them are more severe and are known as haematological malignancies (British...
diarrhea, feeling tired, and muscle cramps. Serious side effects may include abnormal heart rhythms, urinary incontinence, and seizures. Donepezil is a centrally...
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