Difference between revisions of "Derived length"

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Revision as of 00:17, 8 May 2008

This article defines an arithmetic function on a restricted class of groups, namely: solvable groups

Definition

Symbol-free definition

Given a solvable group, we define its solvable length as follows: it is the length of the derived series of the group. Note here that by length of the series, we mean the number of successive inclusions, so the length is one less than the actual number of subgroups in the derived series.