Normal Subgroup

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normal subgroup

[′nȯr·məl ′səb‚grüp]
A subgroup N of a group G where every expression g -1 ng is in N for every g in G and every n in N. Also known as invariant subgroup; normal divisor.

Normal Subgroup


(also normal divisor of a group, invariant subgroup), a fundamental concept of group theory, which was introduced by E. Galois. A normal subgroup of a group G is a subgroup H for which gH = Hg for arbitrary element g of group G.

References in periodicals archive ?
Compared with those in the normal group, serum levels of IL-6 (P<0.01), TNF-[alpha] (P<0.01), NF-[kappa]B (P<0.01), endotoxin (P<0.01), and IL-8 (P<0.05) in the model group increased significantly.
In normal group, serum VDBP levels were higher (594.583+-397.601 ng/ml) compared to osteopenic (348.524+-183.501 ng/ml) and osteoporotic group (278.934+-109.582ng/ml) (p value < 0.0001).
The 25 analyzed variables in the non-normal and normal groups are shown in Table 1.
The normal group and the model group were given normal saline, probiotic group was given probiotics, and the Wumei Pill group was given Wumei Pills.
p-ERK1/2, p-JNK and p-P38 were elevated in the light injury groups, mainly in the ONL, on day 3 and day 5 compared with their levels in normal group [Figure 1]a,[Figure 1]b,[Figure 1]c.{Figure 1}
The frequency of the normal group was found to be higher than encephalitis group on six basic emotions namely (anger, happiness, surprise, disgust and sadness and fear).
Several tissue injuries were noticed in kidney tissues of the newborns treated with gentamicin as compared to the normal group. (Fig.
This may lead to secondary hyperparathyroidism causing increased bone turnover and bone loss.22 Unlike calcium, serum levels of magnesium were not significantly different in the three groups in our study which is similar to some previous findings22 and is in contrast to another study which showed decreased serum levels of magnesium in osteoporotic women compared to the normal group.23
[beta]-catenin mRNA in the IBS group was significantly lower than the Normal group. [beta]-catenin protein expression in C-IBS was similar to the Normal group, while in D-IBS the expression was slightly lower than Normal.
hASCs from 3 independent donors were cultured either in normal medium (normal group) or in medium with a series of cytokines (cytokine group).
Human umbilical vein endothelial cells (HUVECs) were divided into four groups based on treatment, as follows: 200 [micro]g/ml of HSA and 100 mg/dl of glucose (normal group); 200 [micro]g/ml of AGE-HSA and 250 mg/dl of glucose (diabetic group); 200 [micro]g/ml of AGE-HSA and 250 mg/dl of glucose with vitamin D (50 ng/ml) (VD treatment group); and 200 [micro]g/ml of AGE-HSA, 250 mg/dl of glucose, vitamin D (50 ng/ml), and VDR siRNA (VD antagonist group).