# General affine group

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Revision as of 18:39, 22 August 2008 by Vipul (talk | contribs) (New page: {{field-parametrized group property}} {{natural number-parametrized group property}} ==Definition== ===In terms of dimension=== Let <math>n</math> be a natural number and <math>k</...)

*This term associates to every field, a corresponding group property. In other words, given a field, every group either has the property with respect to that field or does not have the property with respect to that field*

*This group property is natural number-parametrized, in other words, for every natural number, we get a corresponding group property*

## Definition

### In terms of dimension

Let be a natural number and be a field. The **general affine group** of order over , denoted or , is defined as the external semidirect product of the vector space by the group , acting by linear transformations.

### In terms of vector spaces

Let be a -vector space (which may be finite- or infinite-dimensional). The general affine group of , denoted , is defined as the external semidirect product of by .