Semidirect Product
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, specifically in the area of abstract algebra known as group theory, a semidirect product is a particular way in which a group can be put together from two subgroups, one of which is a normal subgroup. A semidirect product is a generalization of a direct product. A semidirect product is a cartesian product as a set, but with a particular multiplication operation. If G is the semidirect product of the normal subgroup N and the subgroup H, and both N and ...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, specifically in the area of abstract algebra known as group theory, a semidirect product is a particular way in which a group can be put together from two subgroups, one of which is a normal subgroup. A semidirect product is a generalization of a direct product. A semidirect product is a cartesian product as a set, but with a particular multiplication operation. If G is the semidirect product of the normal subgroup N and the subgroup H, and both N and H are finite, then the order of G equals the product of the orders of N and H. Note that, as opposed to the case with the direct product, a semidirect product of two groups is not, in general, unique; if G and G are two groups which both contain isomorphic copies of N as a normal subgroup and H as a subgroup, and both are a semidirect product of N and H, then it does not follow that G and G are isomorphic. This remark leads to an extension problem, of describing the possibilities.
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