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单词 solvable group
释义

solvable group

A group G is solvable (or soluble) if there exists a sequence of subgroups

such that the quotient groups Gi+1/Gi are abelian groups. For a finite group, this is equivalent to the group's composition factors being cyclic of prime order. It is significant to Galois theory that S5 is not solvable. See Galois group, solvable by radicals.

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更新时间:2025/4/28 19:23:43