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Results tagged with finite-fields
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user 23827
A finite field is a field with a finite number of elements. For each prime power $q^k$, there is a unique (up to isomorphism) finite field with $q^k$ elements. Up to isomorphism, these are the only finite fields.
4
votes
Intersections of products of Sylow $p$-subgroups
The answer to your both questions is 6. Consider the symmetric group $S_3=\langle a,b\mid a^2=b^3=1, b^a=b^{-1}\rangle$, and take $P_1=\langle a\rangle$, $P_2=\langle ab\rangle$, $P_3=\langle ab^2\ran …
- 1,991
3
votes
1
answer
288
views
Number of solutions of a degree 4 polynomial equation over a finite field
Suppose that $q$ is a prime power and $\xi, \eta\in \mathbb{F}_q$ are nonzero. A computer calculation for $q<70$ suggests that the number $N$ of $4$-tuples
$(a,b,c,d)\in\mathbb{F}_q^{4}$ satisfying $( …
- 1,991
2
votes
computer algebra system for polynomial algebras over finite fields
In addition, Magma http://magma.maths.usyd.edu.au/magma/
and GAP http://www.gap-system.org/ will perform these computations.
The former is commercial and the latter is free. If you want to compute
ove …
- 1,991