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 Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
abstract algebra - Prove that $S_3$ and $S_4$ are solvable groups . . . Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
Soluble(solvable) and nilpotent groups - Mathematics Stack Exchange Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
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 . . . Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
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
What exactly does the definition of a nilpotent group mean? I'm studying nilpotent and solvable group and find it pretty hard to tell what the definition of a nilpotent group is after For example, a group is solvable iff it has a solvable series (that is, a subnormal series such that each factor is abelian) This equivalent definition tells something clearly about the structure of the group for me
About solvable groups - Mathematics Stack Exchange For finite groups, an equivalent definition is that a solvable group is a group with a composition series all of whose factors are cyclic groups of prime order This is equivalent because a finite group has finite composition length, and every simple abelian group is cyclic of prime order