of group theory, a solvable group or soluble group is a group that can be constructed from abelian groups using extensions. Equivalently, a solvable group...
18 KB (3,073 words) - 09:51, 27 August 2024
Galois theory (redirect from Solvable by radicals)
of a solvable group in group theory allows one to determine whether a polynomial is solvable in radicals, depending on whether its Galois group has the...
32 KB (4,192 words) - 06:56, 26 June 2024
Divide and conquer breaking down a large, complex problem into smaller, solvable problems Help-seeking obtaining external assistance to deal with obstacles...
86 KB (9,993 words) - 05:55, 5 September 2024
Look up solvable in Wiktionary, the free dictionary. In mathematics, solvable may refer to: Solvable group, a group that can be constructed by compositions...
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subgroup in concept and notation is the solvable radical. The solvable radical is defined to be the largest solvable normal subgroup, and is denoted O ∞ (...
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then any group of order n is solvable. Burnside's theorem, proved using group characters, states that every group of order n is solvable when n is divisible...
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polycyclic group is a solvable group that satisfies the maximal condition on subgroups (that is, every subgroup is finitely generated). Polycyclic groups are...
4 KB (539 words) - 17:45, 23 September 2022
Commutator subgroup (redirect from Derived group)
the case n = 1. A group with G ( n ) ≠ { e } {\displaystyle G^{(n)}\neq \{e\}} for all n in N is called a non-solvable group. A group with G ( α ) = {...
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Quintic function (redirect from Solve quintic equation in general form)
quintics. A solvable quintic is thus an irreducible quintic polynomial whose roots may be expressed in terms of radicals. To characterize solvable quintics...
25 KB (4,164 words) - 13:06, 16 April 2024
nilpotent group is a group that is "almost abelian". This idea is motivated by the fact that nilpotent groups are solvable, and for finite nilpotent groups, two...
15 KB (1,910 words) - 04:48, 10 June 2024