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:
“One should never direct people towards happiness, because happiness too is an idol of the market-place. One should direct them towards mutual affection. A beast gnawing at its prey can be happy too, but only human beings can feel affection for each other, and this is the highest achievement they can aspire to.”
—Alexander Solzhenitsyn (b. 1918)
“Perhaps I am still very much of an American. That is to say, naïve, optimistic, gullible.... In the eyes of a European, what am I but an American to the core, an American who exposes his Americanism like a sore. Like it or not, I am a product of this land of plenty, a believer in superabundance, a believer in miracles.”
—Henry Miller (1891–1980)
“And seniors grow tomorrow
From the juniors today,
And even swimming groups can fade,
Games mistresses turn grey.”
—Philip Larkin (1922–1986)