- direct product of two groups
- прямое произведение двух групп (подмножество декартова произведения элементов групп, на парах которого определена специальная бинарная операция)
Англо-русский словарь промышленной и научной лексики. 2014.
direct product of two groups
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Direct product of groups — Concepts in group theory category of groups subgroups, normal subgroups group homomorphisms, kernel, image, quotient direct product, direct sum semidirect product, wreath product … Wikipedia
Direct product — In mathematics, one can often define a direct product of objects already known, giving a new one. This is generally the Cartesian product of the underlying sets, together with a suitably defined structure on the product set. More abstractly, one… … Wikipedia
direct product — I. noun : scalar product II. noun : cartesian product herein ; especially : a group that is the Cartesian product of two other groups * * * Math. a group, or other such system, every element of which can be written uniquely as the … Useful english dictionary
direct product — noun Date: circa 1925 Cartesian product; especially a group that is the Cartesian product of two other groups … New Collegiate Dictionary
Direct sum of modules — For the broader use of the term in mathematics, see Direct sum. In abstract algebra, the direct sum is a construction which combines several modules into a new, larger module. The result of the direct summation of modules is the smallest general… … Wikipedia
Semidirect product — In mathematics, especially 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… … Wikipedia
Direct sum — The symbol denotes direct sum; it is also the astrological and astronomical symbol for Earth, and a symbol for the Exclusive disjunction. In mathematics, one can often define a direct sum of objects already known, giving a new one. This is… … Wikipedia
Direct sum of groups — In mathematics, a group G is called the direct sum of a set of subgroups {Hi} if each Hi is a normal subgroup of G each distinct pair of subgroups has trivial intersection, and G = <{Hi}>; in other words, G is generated by the subgroups… … Wikipedia
Product (category theory) — In category theory, the product of two (or more) objects in a category is a notion designed to capture the essence behind constructions in other areas of mathematics such as the cartesian product of sets, the direct product of groups, the direct… … Wikipedia
Product of group subsets — In mathematics, one can define a product of group subsets in a natural way. If S and T are subsets of a group G then their product is the subset of G defined by:ST = {st : s in S mbox{ and } tin T}Note that S and T need not be subgroups. The… … Wikipedia
Representation theory of finite groups — In mathematics, representation theory is a technique for analyzing abstract groups in terms of groups of linear transformations. See the article on group representations for an introduction. This article discusses the representation theory of… … Wikipedia
