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  2. Exponentiation - Wikipedia

    en.wikipedia.org/wiki/Exponentiation

    Powers of 2 appear in set theory, since a set with n members has a power set, the set of all of its subsets, which has 2 n members. Integer powers of 2 are important in computer science. The positive integer powers 2 n give the number of possible values for an n-bit integer binary number; for example, a byte may take 2 8 = 256 different values.

  3. Symmetric power - Wikipedia

    en.wikipedia.org/wiki/Symmetric_power

    In linear algebra, the n-th symmetric power of a vector space V is the vector subspace of the symmetric algebra of V consisting of degree-n elements (here the product is a tensor product). In algebraic topology , the n -th symmetric power of a topological space X is the quotient space X n / S n {\displaystyle X^{n}/{\mathfrak {S}}_{n}} , as in ...

  4. Quotient (universal algebra) - Wikipedia

    en.wikipedia.org/wiki/Quotient_(universal_algebra)

    The quotient algebra has these classes as its elements, and the compatibility conditions are used to give the classes an algebraic structure. [ 1 ] The idea of the quotient algebra abstracts into one common notion the quotient structure of quotient rings of ring theory , quotient groups of group theory , the quotient spaces of linear algebra ...

  5. Quotient algebra - Wikipedia

    en.wikipedia.org/wiki/Quotient_algebra

    Quotient algebra may refer to: Specifically, quotient associative algebra in ring theory or quotient Lie algebra; Quotient (universal ...

  6. Quaternion - Wikipedia

    en.wikipedia.org/wiki/Quaternion

    The algebra of quaternions is often ... the quotient quantities p q −1 or q −1 p ... The fourth power of the norm of a quaternion is the determinant of the ...

  7. Cauchy's theorem (group theory) - Wikipedia

    en.wikipedia.org/wiki/Cauchy's_theorem_(group...

    Cauchy's theorem is generalized by Sylow's first theorem, which implies that if p n is the maximal power of p dividing the order of G, then G has a subgroup of order p n (and using the fact that a p-group is solvable, one can show that G has subgroups of order p r for any r less than or equal to n).

  8. Restricted power series - Wikipedia

    en.wikipedia.org/wiki/Restricted_power_series

    In algebra, the ring of restricted power series is the subring of a formal power series ring that consists of power series whose coefficients approach zero as degree goes to infinity. [1] Over a non-archimedean complete field , the ring is also called a Tate algebra .

  9. Quotient group - Wikipedia

    en.wikipedia.org/wiki/Quotient_group

    The quotient group is the same idea, although one ends up with a group for a final answer instead of a number because groups have more structure than an arbitrary collection of objects: in the quotient ⁠ / ⁠, the group structure is used to form a natural "regrouping".

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