PlanetMath (more info)
 Math for the people, by the people. Sponsor PlanetMath
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS  
Login
create new user
name:
pass:
forget your password?
Main Menu
Owner confidence rating: High Entry average rating: No information on entry rating
solvable group (Definition)

A group $G$ is solvable if it has a subnormal series $$ G = G_0 \supset G_1 \supset \cdots \supset G_n = \{1\} $$ where all the quotient groups $G_i/G_{i+1}$ are abelian.




"solvable group" is owned by djao.
(view preamble | get metadata)

View style:

See Also: derived subgroup, composition series, Galois criterion for solvability of a polynomial by radicals

Other names:  solvable, soluble group
Log in to rate this entry.
(view current ratings)

Cross-references: abelian, quotient groups, subnormal series, group
There are 30 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 9316 times total.

Classification:
AMS MSC20A05 (Group theory and generalizations :: Foundations :: Axiomatics and elementary properties)

Pending Errata and Addenda
None.
[ View all 4 ]
Discussion
Style: Expand: Order:
forum policy

No messages.

Interact
post | correct | update request | add derivation | add example | add (any)