Derived subgroup not is purely definable: Difference between revisions
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==History== | ==History== | ||
This is based on as yet unpublished result of Bestvina and Feighn (referred to [http://mathoverflow.net/questions/6925/how-can-we-formalize-the-naturality-of-certain-characteristic-subgroups here]. | This is based on as yet unpublished result of Bestvina and Feighn (referred to [http://mathoverflow.net/questions/6925/how-can-we-formalize-the-naturality-of-certain-characteristic-subgroups here]). | ||
==Statement== | ==Statement== | ||
The [[ | The [[derived subgroup]] of a [[group]] need not be a [[purely definable subgroup]]. | ||
More specifically, the [[ | More specifically, the [[derived subgroup]] of the [[free group:F2|free group of rank two]] is not a purely definable subgroup. | ||
==Related facts== | ==Related facts== | ||
Latest revision as of 04:43, 12 February 2013
This article gives the statement, and possibly proof, of the fact that for a group, the subgroup obtained by applying a given subgroup-defining function (i.e., commutator subgroup) does not always satisfy a particular subgroup property (i.e., purely definable subgroup)
View subgroup property satisfactions for subgroup-defining functionsView subgroup property dissatisfactions for subgroup-defining functions
History
This is based on as yet unpublished result of Bestvina and Feighn (referred to here).
Statement
The derived subgroup of a group need not be a purely definable subgroup.
More specifically, the derived subgroup of the free group of rank two is not a purely definable subgroup.