solvable group

(redirected from Solvable subgroup)

solvable group

[′säl·və·bəl ′grüp]
(mathematics)
A group G which has subgroups G0, G1,…, Gn , where G0= G, Gn = the identity element alone, and each Gi is a normal subgroup of Gi-1with the quotient group Gi-1/ Gi Abelian.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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By results of Mal'cev and Auslander, it is known that a group G is polycyclic if and only if G is realizable as a solvable subgroup of GL(n, Z), cf.
If F is a solvable subgroup of GL (n, Z[1/p]), does [GAMMA] admit a controlled Folner sequence?
Let G be a complex semisimple Lie group, let B be a Borel subgroup of G, i.e., a maximal solvable subgroup, and T be a maximal torus contained in B.