Direct Product Of Groups
In the mathematical field of group theory, the direct product is an operation that takes two groups G and H and constructs a new group, usually denoted G × H. This operation is the group-theoretic analogue of the Cartesian product of sets, and is one of several important notions of direct product in mathematics.
In the context of abelian groups, the direct product is sometimes referred to as the direct sum, and is denoted G ⊕ H. Direct sums play an important role in the classification of abelian groups: according to fundamental theorem of finite abelian groups, every finite abelian group can be expressed as the direct sum of cyclic groups.
Read more about Direct Product Of Groups: Definition, Examples, Elementary Properties, Algebraic Structure
Famous quotes containing the words direct, product and/or groups:
“Parliament must not be told a direct untruth, but it’s quite possible to allow them to mislead themselves.”
—Norman Tebbit (b. 1931)
“The product of mental labor—science—always stands far below its value, because the labor-time necessary to reproduce it has no relation at all to the labor-time required for its original production.”
—Karl Marx (1818–1883)
“And seniors grow tomorrow
From the juniors today,
And even swimming groups can fade,
Games mistresses turn grey.”
—Philip Larkin (1922–1986)