The Vedic Square can be viewed as the multiplication table of the monoid where is the set of positive integers partitioned by the residue classes modulo nine. (the operator refers to the abstract "multiplication" between the elements of this monoid).
If are elements of then can be defined as , where the element 9 is representative of the residue class of 0 rather than the traditional choice of 0.
This does not form a group because not every non-zero element has a corresponding inverse element; for example but there is no such that .
Properties of subsets
The subset forms a cyclic group with 2 as one choice of generator - this is the group of multiplicative units in the ring . Every column and row includes all six numbers - so this subset forms a Latin square.
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| 1 | 2 | 4 | 5 | 7 | 8 |
1 |
1 | 2 | 4 | 5 | 7 | 8 |
2 |
2 | 4 | 8 | 1 | 5 | 7 |
4 |
4 | 8 | 7 | 2 | 1 | 5 |
5 |
5 | 1 | 2 | 7 | 8 | 4 |
7 |
7 | 5 | 1 | 8 | 4 | 2 |
8 |
8 | 7 | 5 | 4 | 2 | 1 |
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