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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A solvable group has a subnormal series of subgroups.
5 and the smallest non solvable group containing four conjugacy classes.
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]).
Abels:1971] Abels Herbert, 1971, An example of a finitely presented solvable group, London Mathematical Society lecture notes, Cambridge: Cambridge University Press, pp.
cocompact lattice) of a direct product of a p-adic solvable group with a connected, solvable Lie group.
3 shows that there exists a solvable group [GAMMA] such that W([GAMMA]) contains S[L.
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.
We begin by proving that the generalized free product of a nilpotent group and a solvable group is not necessarily perfect.
Here we recall that every binary solvable group except [Q.
And for a general connected solvable group S, the Lie subalgebra t [intersection] [s, s] is always central in s.
Let G be a solvable group in which [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], for 1 [less than or equal to] [[alpha].
Let G be a solvable group, then one of the following holds.