| 1 | a | b | b2 | b3 | b4 | |
|---|---|---|---|---|---|---|
| 1 | 1 | a | b | b2 | b3 | b4 |
| a | a | a | b | b2 | b3 | b4 |
| b | b | b | b2 | b3 | b4 | b |
| b2 | b2 | b2 | b3 | b4 | b | b2 |
| b3 | b3 | b3 | b4 | b | b2 | b3 |
| b4 | b4 | b4 | b | b2 | b3 | b4 |
| Length: | Presentation: | Description: | Related: |
|---|---|---|---|
| 6 | 〈a, b | ab=aa, bb=1〉 | Finite non-commutative monoid with 6 elements | 22 isomorphic |
| 6 | 〈a, b | aaa=1, abb=1〉 | Isomorphic to ℤ6 | 1373 isomorphic |
| 6 | 〈a, b | aa=1, abb=b〉 | Finite non-commutative monoid with 6 elements | 30 isomorphic |
| 7 | 〈a, b | ab=aa, bb=b〉 | Finite non-commutative monoid with 6 elements | |
| 7 | 〈a, b | aa=a, bbb=a〉 | Finite commutative monoid with 6 elements | 49 isomorphic |
| 7 | 〈a, b | aa=b, bbb=a〉 | Finite commutative monoid with 6 elements | 61 isomorphic |
| 7 | 〈a, b | aa=b, bbb=b〉 | Finite commutative monoid with 6 elements | 55 isomorphic |
| 7 | 〈a, b | aa=1, abab=b〉 | Finite non-commutative monoid with 6 elements | 31 isomorphic, 22 anti-isomorphic |
| 8 | 〈a, b | ab=aa, baa=b〉 | Finite non-commutative monoid with 6 elements | 4 isomorphic |
| 8 | 〈a, b | ab=aa, bbb=a〉 | Finite commutative monoid with 6 elements | 46 isomorphic |
| 8 | 〈a, b | aa=a, abbb=b〉 | Finite non-commutative monoid with 6 elements | 19 isomorphic |
| 8 | 〈a, b | aa=a, aab=bb〉 | Finite non-commutative monoid with 6 elements | 3 isomorphic |
| 8 | 〈a, b | ab=a, baa=bb〉 | Finite non-commutative monoid with 6 elements | 12 isomorphic, 1 anti-isomorphic |
| 9 | 〈a, b | abba=b, baba=1〉 | Finite non-Abelian group with 6 elements | 66 isomorphic |
| 9 | 〈a, b | aaa=aa, abb=b〉 | Finite non-commutative monoid with 6 elements | 5 isomorphic |
| 9 | 〈a, b | aab=bb, abb=a〉 | Finite commutative monoid with 6 elements | 13 isomorphic |
| 9 | 〈a, b | aba=aa, baa=b〉 | Finite non-commutative monoid with 6 elements | |
| 9 | 〈a, b | abb=aa, bbb=a〉 | Finite commutative monoid with 6 elements | 49 isomorphic |
| 9 | 〈a, b | ab=a, aaaa=bb〉 | Finite commutative monoid with 6 elements | 14 isomorphic |
| 9 | 〈a, b | ab=a, bbbb=aa〉 | Finite commutative monoid with 6 elements | 5 isomorphic |
| 9 | 〈a, b | ab=a, bbbb=ba〉 | Finite non-commutative monoid with 6 elements | 2 isomorphic |
| 9 | 〈a, b | ab=a, bbb=aaa〉 | Finite commutative monoid with 6 elements | 9 isomorphic |
| 9 | 〈a, b | ab=a, bbb=bba〉 | Finite non-commutative monoid with 6 elements | 3 isomorphic |
| 10 | 〈a, b | aba=aa, aabb=b〉 | Finite non-commutative monoid with 6 elements | 5 isomorphic |
| 10 | 〈a, b | aab=b, aaba=aa〉 | Finite non-commutative monoid with 6 elements | 1 isomorphic |