Example
The cyclic group of order 8 has the presentation
But, up to isomorphism there are three more groups that "satisfy" the relation namely:
- and
However none of these satisfy the irrelation . So an absolute presentation for the cyclic group of order 8 is:
It is part of the definition of an absolute presentation that the irrelations are not satisfied in any proper homomorphic image of the group. Therefore:
Is not an absolute presentation for the cyclic group of order 8 because the irrelation is satisfied in the cyclic group of order 4.
Read more about this topic: Absolute Presentation Of A Group
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“Our intellect is not the most subtle, the most powerful, the most appropriate, instrument for revealing the truth. It is life that, little by little, example by example, permits us to see that what is most important to our heart, or to our mind, is learned not by reasoning but through other agencies. Then it is that the intellect, observing their superiority, abdicates its control to them upon reasoned grounds and agrees to become their collaborator and lackey.”
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