Baer-Specker group: Difference between revisions
(New page: {{particular group}} ==Definition== The '''Baer-Specker group''' is defined as the external direct product of countably many copies of the group of integers. ==Facts== * [[Baer...) |
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The '''Baer-Specker group''' is defined as the [[external direct product]] of countably many copies of the [[group of integers]]. | The '''Baer-Specker group''' is defined as the [[external direct product]] of countably many copies of the [[group of integers]]. | ||
==Arithmetic functions== | |||
{| class="wikitable" border="1" | |||
! Function !! Value !! Explanation | |||
|- | |||
| [[order of a group|order]] || infinite (uncountable) || | |||
|- | |||
| [[exponent of a group|exponent]] || infinite || | |||
|- | |||
| [[Frattini length]] || [[arithmetic function value::Frattini length;1|1]] || | |||
|- | |||
| [[Fitting length]] || [[arithmetic function value::Fitting length;1|1]] || | |||
|} | |||
==Group properties== | |||
{| class="wikitable" border="1" | |||
! Property !! Satisfied !! Explanation | |||
|- | |||
| [[satisfies property::abelian group]] || Yes || | |||
|- | |||
| [[satisfies property::nilpotent group]] || Yes || | |||
|- | |||
| [[dissatisfies property::finitely generated group]] || No || | |||
|} | |||
==Facts== | ==Facts== | ||
* [[Baer-Specker group is not free | * [[Baer-Specker group is not free abelian]] | ||
Latest revision as of 02:01, 10 September 2009
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Definition
The Baer-Specker group is defined as the external direct product of countably many copies of the group of integers.
Arithmetic functions
| Function | Value | Explanation |
|---|---|---|
| order | infinite (uncountable) | |
| exponent | infinite | |
| Frattini length | 1 | |
| Fitting length | 1 |
Group properties
| Property | Satisfied | Explanation |
|---|---|---|
| abelian group | Yes | |
| nilpotent group | Yes | |
| finitely generated group | No |