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solvable group (Definition)

A group $ G$ is solvable if it has a subnormal series

$\displaystyle G = G_0 \supset G_1 \supset \cdots \supset G_n = \{1\} $
where all the quotient groups $ G_i/G_{i+1}$ are abelian.



"solvable group" is owned by djao.
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See Also: derived subgroup, composition series, Galois criterion for solvability of a polynomial by radicals

Other names:  solvable, soluble group
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Cross-references: abelian, quotient groups, subnormal series, group
There are 28 references to this entry.

This is version 7 of solvable group, born on 2002-01-05, modified 2006-04-30.
Object id is 1336, canonical name is Solvable.
Accessed 7474 times total.

Classification:
AMS MSC: 20A05 (Group theory and generalizations :: Foundations :: Axiomatics and elementary properties)
Pending Errata and Addenda
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