PlanetMath: supersolvable group

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supersolvable group

(Definition)

A group $G$ is supersolvable if it has a finite normal series $$G = G_0 \rhd G_1 \rhd \cdots \rhd G_n = 1$$ with the property that each factor group $G_{i-1}/G_i$ is cyclic.

A supersolvable group is solvable.

"supersolvable group" is owned by mclase.

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supersolvable

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Cross-references: nilpotent groups, finitely generated, solvable, cyclic, factor group, property, normal series, finite, group
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This is version 2 of supersolvable group, born on 2003-10-04, modified 2004-10-22.
Object id is 4751, canonical name is SupersolvableGroup.
Accessed 3315 times total.

Classification:

AMS MSC:	20F16 (Group theory and generalizations :: Special aspects of infinite or finite groups :: Solvable groups, supersolvable groups)
	20D10 (Group theory and generalizations :: Abstract finite groups :: Solvable groups, theory of formations, Schunck classes, Fitting classes, $\pi$-length, ranks)

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