Center is elementarily characteristic: Difference between revisions
(New page: {{sdf subgroup property satisfaction| sdf = center| property = elementarily characteristic subgroup}} ==Statement== The center of a group is an [[elementarily characteristic subg...) |
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The [[center]] of a [[group]] is an [[elementarily characteristic subgroup]]: there is no other subgroup of the group that is [[elementarily | The [[center]] of a [[group]] is an [[elementarily characteristic subgroup]]: there is no other subgroup of the group that is [[elementarily equivalently embedded subgroups|elementarily equivalently embedded]]. | ||
Latest revision as of 22:22, 2 December 2008
This article gives the statement, and possibly proof, of the fact that for any group, the subgroup obtained by applying a given subgroup-defining function (i.e., center) always satisfies a particular subgroup property (i.e., elementarily characteristic subgroup)}
View subgroup property satisfactions for subgroup-defining functionsView subgroup property dissatisfactions for subgroup-defining functions
Statement
The center of a group is an elementarily characteristic subgroup: there is no other subgroup of the group that is elementarily equivalently embedded.