solvable group


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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.
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References in periodicals archive ?
A solvable group has a subnormal series of subgroups.
From finite groups to finite-dimensional Hopf algebras
5 and the smallest non solvable group containing four conjugacy classes.
A SIMPLE PROOF OF A5 AS A SUBGROUP OF S7 BY USING HARACTER TABLE OF S7
Recently, Guo and Shum pushed further this approach and obtained some charaterizations for a solvable group and a p-solvable group based on the assumption that some of its subgroups are CAP-subgroups (see [7]).
The influence of SCAP and S-supplemented subgroups on the p-nilpotency of finite groups
Abels:1971] Abels Herbert, 1971, An example of a finitely presented solvable group, London Mathematical Society lecture notes, Cambridge: Cambridge University Press, pp.
Finite c-groups
cocompact lattice) of a direct product of a p-adic solvable group with a connected, solvable Lie group.
On the ergodic theorem for affine actions on Hilbert space
3 shows that there exists a solvable group [GAMMA] such that W([GAMMA]) contains S[L.
Invariant means for the wobbling group
A long standing open problem in the character theory of finite solvable groups is whether the derived length dl(G) of a solvable group G is bounded above by the cardinality of cd(G), the set of irreducible character degrees of that group, i.
Some sufficient conditions for the Taketa inequality
We begin by proving that the generalized free product of a nilpotent group and a solvable group is not necessarily perfect.
On the residual solvability of generalized free products of solvable groups
Here we recall that every binary solvable group except [Q.
On 2-pyramidal Hamiltonian cycle systems
And for a general connected solvable group S, the Lie subalgebra t [intersection] [s, s] is always central in s.
On the equivalence of several definitions of compact infra-solvmanifolds
Let G be a solvable group in which [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], for 1 [less than or equal to] [[alpha].
Subgroup S-commutativity degrees of finite groups
Let G be a solvable group, then one of the following holds.
Finite groups containing certain abelian TI-subgroups

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