- #1
hihiip201
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We have the 3 equivalent definition for solvable groups:
There exists a chain of subgroups
1 < G1 ...< Gi + < G i+1 < Gr = G
such that Gi is normal in Gi+1 and Gi+1/Gi is abelian.
Another definition is
there exists
1 < H1 ...< Hi + < H i+1 < Hs = H
such that Hi is normal in Hi+1, and Hi+1/Hi is cyclic
, the last definition is similar but the quotient group is isomorphic to Z/p.
so my question is, does s need to be equal r?
thanks
There exists a chain of subgroups
1 < G1 ...< Gi + < G i+1 < Gr = G
such that Gi is normal in Gi+1 and Gi+1/Gi is abelian.
Another definition is
there exists
1 < H1 ...< Hi + < H i+1 < Hs = H
such that Hi is normal in Hi+1, and Hi+1/Hi is cyclic
, the last definition is similar but the quotient group is isomorphic to Z/p.
so my question is, does s need to be equal r?
thanks