Show is a solvable group.

The group operation is matrix multiplication.

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- Apr 12th 2010, 11:27 AMmathman88Solvable Group
Show is a solvable group.

The group operation is matrix multiplication. - Apr 12th 2010, 11:38 AMtonio
- Apr 12th 2010, 11:47 AMmathman88
- Apr 12th 2010, 11:58 AMtonio
- Apr 12th 2010, 12:02 PMmathman88
- Apr 12th 2010, 12:14 PMtonio

This is not the usual definition, and it's a rather misleading and even incorrect one (imo, of course. See following note), but it never minds: since the group is finitely generated then is finitely generated and thus can be decomposed in a direct product of cyclic groups...

Note: for your definition to work it MUST be that G is fin. generated, or at least that all its abelian factor groups are, otherwise it fails: an infinitely generated abelian group wouldn't be solvable according to your definition which, of course, is absurd.

Tonio