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Subgroup analysis refers to repeating the analysis of a study within subgroups of subjects defined by a subgrouping variable. For example: smoking status defining two subgroups: smokers and non-smokers.
For example, the subgroup Z 7 of the non-abelian group of order 21 is normal (see List of small non-abelian groups and Frobenius group#Examples). An alternative proof of the result that a subgroup of index lowest prime p is normal, and other properties of subgroups of prime index are given in .
The hidden subgroup problem (HSP) is a topic of research in mathematics and theoretical computer science. The framework captures problems such as factoring , discrete logarithm , graph isomorphism , and the shortest vector problem .
A core-free subgroup is a subgroup whose normal core is the trivial subgroup. Equivalently, it is a subgroup that occurs as the isotropy subgroup of a transitive, faithful group action. The solution for the hidden subgroup problem in the abelian case generalizes to finding the normal core in case of subgroups of arbitrary groups.
One of the best-known examples of Simpson's paradox comes from a study of gender bias among graduate school admissions to University of California, Berkeley.The admission figures for the fall of 1973 showed that men applying were more likely than women to be admitted, and the difference was so large that it was unlikely to be due to chance.
A proper subgroup of a group G is a subgroup H which is a proper subset of G (that is, H ≠ G). This is often represented notationally by H < G, read as "H is a proper subgroup of G". Some authors also exclude the trivial group from being proper (that is, H ≠ {e} ). [2] [3] If H is a subgroup of G, then G is sometimes called an overgroup of H.
Let V be the non-cyclic subgroup of A 4 called the Klein four-group. V = {e, (1 2)(3 4), (1 3)(2 4), (1 4)(2 3)}. Let K = H ⋂ V. Since both H and V are subgroups of A 4, K is also a subgroup of A 4. From Lagrange's theorem, the order of K must divide both 6 and 4, the orders of H and V respectively. The only two positive integers that divide ...
As this is a logical (deterministic) and not a statistical (probabilistic) technique, with "crisp-set" QCA , the original application of QCA, variables can only have two values, which is problematic as the researcher has to determine the values of each variable. For example: GDP per capita has to be divided by the researcher in two categories ...