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- How to determine if a linear system is solvable
So "showing a system of linear equations is not solvable" (has no solutions) is, by definition, the same thing as showing that the system of linear equations is "inconsistent" "A system doesn't have a unique solution" can happen in two ways: it can have more than one solution (in which case it has infinitely many solutions), or it can have no
- $S_3$ is soluable but not nilpotent - Mathematics Stack Exchange
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- abstract algebra - Prove that $S_3$ and $S_4$ are solvable groups . . .
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- Soluble(solvable) and nilpotent groups - Mathematics Stack Exchange
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- Are all polynomials solvable? - Mathematics Stack Exchange
$\begingroup$ @Dario: in fact, have you ever tried to use the cubic formula on an actual cubic polynomial? The first or second time I tried to do this I found I had to take the cube root of an imaginary number and I could only write the roots of the polynomial in terms of cos pi 9, which is itself the root of an irreducible cubic polynomial; so I end up not much better off than when I started!
- Definitions of solvable group - Mathematics Stack Exchange
A solvable group seems to be variously defined as one with a composition series where all the composition factors are Abelian, or as one with a subnormal series where all the quotients are Abelian Unlike with the first definition, this definition does not explicitly seem to require that the quotients be simple
- abstract algebra - Subgroups of finite solvable groups. Solvable . . .
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- What does insolvability of the quintic mean exactly?
The definition of solvable group won't mean much to you if you haven't done a course in group theory; there should be a sequence of groups, starting with the trivial group and ending with the group corresponding to the polynomial, such that each group in the sequence is a "normal" subgroup of the next group, and the "quotient" of each group by
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